Answers
Answer:
Below are the exact values of sine, cosine, and tangent of the given angle -11π/12.
[tex]sin(-\frac{11\pi}{12})=\frac{-\sqrt{6}+\sqrt{2}}{4}[/tex][tex]cos(-\frac{11\pi}{12})=\frac{-\sqrt{6}-\sqrt{2}}{4}[/tex][tex]tan(-\frac{11\pi}{12})=\frac{sin(-\frac{11\pi}{12})}{cos(-\frac{11\pi}{12})}=2-\sqrt{3}[/tex]Explanation:
We can use the following trigonometric identities to solve the exact value of the given angle.
[tex]\begin{gathered} sin(x+y)=sin\text{ }x\text{ }cos\text{ }y+cos\text{ }x\text{ }sin\text{ }y \\ cos(x+y)=cos\text{ }x\text{ }cos\text{ }y-sin\text{ }x\text{ }sin\text{ }y \end{gathered}[/tex]For sine function, we have:
[tex]\begin{gathered} sin(-\frac{11\pi}{12})=sin(\frac{\pi}{4}-\frac{7\pi}{6}) \\ sin(\frac{\pi}{4}-\frac{7\pi}{6})=sin\text{ }\frac{\pi}{4}cos(-\frac{7\pi}{6})+cos\text{ }\frac{\pi}{4}sin(-\frac{7\pi}{6}) \end{gathered}[/tex]Simplify.
[tex]\begin{gathered} sin(\frac{\pi}{4}-\frac{7\pi}{6})=\frac{\sqrt{2}}{2}(-\frac{\sqrt{3}}{2})+\frac{\sqrt{2}}{2}(\frac{1}{2}) \\ sin(\frac{\pi}{4}-\frac{7\pi}{6})=\frac{-\sqrt{6}}{4}+\frac{\sqrt{2}}{4} \\ sin(\frac{\pi}{4}-\frac{7\pi}{6})=\frac{-\sqrt{6}+\sqrt{2}}{4} \\ sin(-\frac{11\pi}{12})=\frac{-\sqrt{6}+\sqrt{2}}{4} \end{gathered}[/tex]For cosine function, we have:
[tex]\begin{gathered} cos(-\frac{11\pi}{12})=cos(\frac{\pi}{4}-\frac{7\pi}{6}) \\ cos(\frac{\pi}{4}-\frac{7\pi}{6})=cos\frac{\pi}{4}cos(-\frac{7\pi}{6})-sin\frac{\pi}{4}sin(-\frac{7\pi}{6}) \end{gathered}[/tex]Simplify.
[tex]\begin{gathered} cos(\frac{\pi}{4}-\frac{7\pi}{6})=\frac{\sqrt{2}}{2}(-\frac{\sqrt{3}}{2})-(\frac{\sqrt{2}}{2})(\frac{1}{2}) \\ cos(\frac{\pi}{4}-\frac{7\pi}{6})=\frac{-\sqrt{6}}{4}-\frac{\sqrt{2}}{4} \\ cos(\frac{\pi}{4}-\frac{7\pi}{6})=\frac{-\sqrt{6}-\sqrt{2}}{4} \\ cos(-\frac{11\pi}{12})=\frac{-\sqrt{6}-\sqrt{2}}{4} \end{gathered}[/tex]Lastly, for tangent function, it is the ratio between sine and cosine function.
[tex]tan(-\frac{11\pi}{12})=\frac{sin(-\frac{11\pi}{12})}{cos(-\frac{11\pi}{12})}[/tex]Applying the division rule, we get the reciprocal of the denominator and multiply it to the numerator. The equation becomes:
[tex]tan(-\frac{11\pi}{12})=sin(-\frac{11\pi}{12})\times\frac{1}{cos(-\frac{11\pi}{12})}[/tex]Now, let's replace the sine and cosine value that we have calculated above.
[tex]tan(-\frac{11\pi}{12})=\frac{-\sqrt{6}+\sqrt{2}}{4}\times\frac{4}{-\sqrt{6}-\sqrt{2}}[/tex]Since 4 is a common factor on both numerator and denominator, we can cancel it out. The equation then becomes,
[tex]tan(-\frac{11\pi}{12})=\frac{-\sqrt{6}+\sqrt{2}}{-\sqrt{6}-\sqrt{2}}[/tex]To further simplify the function, let's remove the radicals in the denominator by rationalization.
[tex]\begin{gathered} tan(-\frac{11\pi}{12})=\frac{-\sqrt{6}+\sqrt{2}}{-\sqrt{6}-\sqrt{2}}\times\frac{-\sqrt{6}+\sqrt{2}}{-\sqrt{6}+\sqrt{2}} \\ tan(-\frac{11\pi}{12})=\frac{6-\sqrt{12}-\sqrt{12}+2}{6-\sqrt{12}+\sqrt{12}-2} \end{gathered}[/tex][tex]\begin{gathered} tan(-\frac{11\pi}{12})=\frac{8-2\sqrt{12}}{4} \\ tan(-\frac{11\pi}{12})=\frac{8-2\sqrt{4\times3}}{4} \\ tan(-\frac{11\pi}{12})=\frac{8-(2\times2\sqrt{3})}{4} \\ tan(-\frac{11\pi}{12})=\frac{8-4\sqrt{3}}{4} \\ Factor\text{ }4\text{ }in\text{ }the\text{ }numerator. \\ tan(-\frac{11\pi}{12})=\frac{4(2-\sqrt{3})}{4} \\ Cancel\text{ }4. \\ tan(-\frac{11\pi}{12})=2-\sqrt{3} \end{gathered}[/tex]Related Questions
find the area of the triangle, carry your internediate computations to at least four decimal places round your answer to the nearest tenth
Answers
Heron's formula is defined as:
[tex]\begin{gathered} A=\sqrt[]{s(s-a)(s-b)(s-c)} \\ \text{where} \\ a,b,\text{ and }c\text{ are the three sides of the triangle} \\ s=\frac{a+b+c}{2} \end{gathered}[/tex]Given: sides with length 12 yd, 14 yd, 15 yd.
Then
[tex]\begin{gathered} s=\frac{12+14+15}{2} \\ s=\frac{41}{2} \\ s=20.5\text{ yd} \end{gathered}[/tex]Plugin the following values to Heron's formula and we get
[tex]\begin{gathered} A=\sqrt[]{s(s-a)(s-b)(s-c)} \\ A=\sqrt[]{20.5(20.5-12)(20.5-14)(20.5-15)} \\ A=\sqrt[]{20.5(8.5)(6.5)(5.5)} \\ A=78.926785694085\text{ yd}^2 \\ \text{Rounded this off to the nearest tenth and we get} \\ A=78.9\text{ yd}^2 \end{gathered}[/tex]When something is NOT stated explicitly in a text, and a reader has to use evidence in the text to figure out the meaning, it is called _____.
.jumping to a conclusion
.making an inference
.searching for connotations
.creating mental pictures
Answers
Answer:
making an inference is the correct answer.
Step-by-step explanation:
Are the ratios 5:2 and 15:6 equivalent?
Answers
Answer:
Yes
Step-by-step explanation:
5 x 3= 15
2 x 3= 6
Since they are multiplied by the same number to get to 15/6 they are equivalent fractions
Factor completely 3x^2+9x-54
Answers
Answer:
(3x+18)(x-3)
Step-by-step explanation:
3x^2 + 9x - 54 = 0
x^2 + 3x - 18 = 0
(x+6)(x-3) = 0
x = -6
x = 3
3(x-(-6)(x-3)
3(x+6)(x-3)
(3x+18)(x-3)
Can somone please help me with this, find x.
Answers
Answer:
11. x=13; 12. x=30; 13. 9
Step-by-step explanation:
Thirty increases by a number t.
Write a variable expression for the word problem
Answers
Answer:
30 + t;
Step-by-step explanation:
Thirty increases by a number t.
This means 30 is more than t, therefore (so), 30 + t.
A 20-oz bottle of shampoo cost $2.90. A 12-oz bottle costs $1.35. Which is the better buy?
Answers
The price of each ounce of shampoo for the 20-oz bottle is:
[tex]\frac{2.90}{20}=0.145.[/tex]And the price of each ounce of shampoo for the 12-oz bottle is:
[tex]\frac{1.35}{12}=0.1125[/tex]Answer: The 12-oz bottle is the best buy.
use formula of boolean 1+1
Answers
Answer:
i know i answered this but a mod must have got rid of it it is 1
Step-by-step explanation:
Jason sold 2/3 of his baseball card collection. What is this amount as a decimal?
Answers
Answer:
ABOUT 0.6666666666666666667
Answer: The 2/3 fraction as a decimal is 0.666666666667
The amount of cards as a decimal is unknown (need quantity info)
Step-by-step explanation:
The 2/3 fraction in decimal form can be rounded to the proper degree of precision (such as .67 for hundredths).
which value of R makes the right side of the equation equal to 27,000?a)210,000b)220,000c)200,000d)183,000
Answers
Given:
The equation is
[tex]27000=R-183000[/tex]Find-:
The value of "R."
Explanation-:
The "R" is
[tex]\begin{gathered} 27000=R-183000 \\ \\ 27000+183000=R-183000+183000 \\ \\ R=210000 \end{gathered}[/tex]The value of "R" is 210000.
So, the expression is:
[tex]\begin{gathered} 27000=R-183000 \\ \\ 27000=210000-183000 \\ \\ 27000=27000 \end{gathered}[/tex]Is (2, – 7) a solution to this system of equations? 5x+2y=7 13x+5y= – 9
Answers
Answer:False.
Step-by-step explanation:
Multiply both sides of the equation by a coefficient:begin equation begin cases5 5 x + 2 y = 7 * 52 13.
9x + 3y = 14 what is y
Answers
how many quarts are in 12 pints
Answers
Answer:
6
Step-by-step explanation:
12/2=6
Factor the expression completely.
5x - 5x-10
Please explain this step by step
Answers
Answer:
\textcolor{#B14BA5}{5x}\textcolor{#B14BA5}{-5x}-10
5
−
5
−
1
0
-10
−
1
0
Answer:
Step-by-step explanation:
5x^2 - 5x - 10
factor out the 5
5 (x^2 - x -2 )
note how the 5 doesn't make any difference for our question.
now use FOIL , know it?
First, Outside, Inside, Last
(X ± ? ) * ( X ± ? )
we want that above form.
(X+1) * (X - ? )
hmm
(X+1) * (X -2)
that looks like it would work
now just put the 5 back on
5*{(X+1)*(X-2)}
there it is :)
WILL GIVE BRAINLIEST please rewrite the hypothesis for all 3
Answers
Answer:
if the egg was the same size then that must mean the eggs had different reactions than each other.
Step-by-step explanation:
Casho is trying to find the height of a radio antenna on the roof of a local
building. She stands at a horizontal distance of 26 meters from the building.
The angle of elevation from her eyes to the roof (point A) is 32°, and the
angle of elevation from her eyes to the top of the antenna (point B) is 36°. If
her eyes are 1.75 meters from the ground, find the height of the antenna (the
distance from point A to point B). Round your answer to the nearest meter if
necessary.
Answers
Distance from point A to point B is approx. 3m
What is the difference between Distance and Displacement?
While distance and displacement appear to signify the same thing, they actually have very different definitions and meanings.
A scalar quantity known as distance measures "how much ground an object has traversed" while moving.
An object's total change in position is referred to as displacement, a vector variable that measures "how far out of place an object is."
Distance is the sum of an object's movements, regardless of direction. Regardless of an object's starting or ending position, distance can be defined as the amount of ground it has covered.
The term "displacement" refers to a shift in an object's position. It is a vector quantity with a magnitude and direction. The symbol for it is an arrow pointing from the initial location to the ending place. For instance, if an object shifts from location A to position B, its position changes. Displacement is the term used to describe this shift in an object's position.
∠BCD = 36°
∠ACD = 32°
CD= 26m
tan∠BCD=0.726
tan∠ACD=0.624
since,
BD=CD x tan∠BCD
AD=CD x tan∠ACD
thus,
AB = BD-AD
= CD x tan∠BCD - CD x tan∠ACD
= CD x [0.726 - 0.624]
= 2.652
= approx 3 m
Learn more about Distance nd displacement from the link below
https://brainly.com/question/3243551
#SPJ9
Answer:
3(m)
Step-by-step explanation:
fills a 50gallon fish tank completely with water only to find that it has a
leak in the bottom. The leak is draining one gallon of water every two hours. Write an
equation that shows how many gallons of water are left in the tank:
Answers
The equation that shows the amount of water in gallons remaining in the water tank in terms of time t is A = 50 - t/2.
How to form an equation?Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.
As per the given,
Amount of water initially = 50 gallons
Leakage of water in 2 hours = 1 gallon.
Leakage in t hour = t/2 gallons.
Thus,
Amount = 50 - t/2
A = 50 - t/2
Hence "The equation that shows the amount of water in gallons remaining in the water tank in terms of time t is A = 50 - t/2".
For more about the equation,
https://brainly.com/question/10413253
#SPJ1
Are this triangles similar?
Answers
Answer: yes
Step-by-step explanation:
yes
Using the graph as your guide, complete the following statement.
The discriminant of the function is
• A. negative
• B. zero
• C. positive
Answers
Answer:
B. Negative
Step-by-step explanation:
A discriminant of zero indicates that the quadratic has a repeated real number solution. A negative discriminant indicates that neither of the solutions is a real number.
Umbrellas inLost and FoundNumber of sunny daysWhat conclusion can you make about the relationship between the variables?O A. As the number of sunny days increases, the number of lostumbrellas tends to increase.B. An increase in lost umbrellas causes a decrease in the number ofsunny days.C. As the number of sunny days increases, the number of lostumbrellas tends to decrease.D. An increase in the number of sunny days causes a decrease inlost umbrellas
Answers
From the given figure, we observe that,
The relationship between the variables is,
As the number of sunny days increases, the number of lost umbrellas tends to decrease.
Hence, the correct option is C.
help meeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
Answers
Answer: 2.5, 5.3
Step-by-step explanation:
[tex]-16t^2 +126t=217\\ \\ 16t^2 -126t+217=0\\\\t=\frac{-(-126) \pm \sqrt{(-126)^2 -4(16)(217)}}{2(16)}\\\\t \approx 2.5, 5.3[/tex]
If P = (-1,5), Find:Ry=1 (P)([?], []).
Answers
The line y = 1 is a horizontal line and thus is a line that is parallel to the x-axis.
If we reflect about a line that is parallel to the x-axis, then the x-coordinate of the point (that is reflected) will remain the same, thus the image of (-1, 5) has x-coordinate -1 and thus the point is of the form (-1, b).
The point (-1, 5) is 4 units from the line y = 1 (because the difference between y = 5 and y = 1 is 4).
The reflected point has to be the same distance from the line y = 1 as the original point
what is the place value of digit 3 in the number 73892
Answers
answer:
the digit 3 is in the thousands place in the number 73,892.
step-by-step explanation:
the answer was determined based on the definition of the thousands place. it may be easier to tell with a comma in place. hope that helps!
Please help on this, it's like for maths
Answers
Answer:
1.48
Step-by-step explanation:
Subtract 14 from 32 giving us 18. Showing us that 18 is the amount of girls in the class.
Then do 32 x 1.515 which gives us 48.48
multiply the 14 x 1.56 = 21.84
then do 48.48 - 21.84 =26.64
then do 26.62 divided by 18
which gives us 1.48.
An investment of $2,400 earns interest at the rate of 2.8% and is compounded daily. What is the accumulated value of the investment at the end of 6 years?
Answers
Which of the following is the average rate of change over the interval [−3, 0] for the function g(x) = log2(x + 4) − 5? (2 points)
Answers
The average rate of change of g(x) on the interval [-3, 0] is r = 2/3.
How to get the average rate of change?
For any function f(x), we define the average rate of change on an interval [a, b] as:
r = ( f(b) - f(a))/(b - a)
In this case, the interval is [-3, 0], and the function is:
g(x) = log₂(x + 4) - 5
Replacing that in the average rate of change formula, we get:
r = ( g(0) - g(-3))/(0 + 3)
g(0) = log₂(0 + 4) - 5 = -3
g(-3) = log₂(-3 + 4) - 5 = -5
Replacing that:
r = (-3 + 5)/3 = 2/3
The average rate of change is 2/3.
Learn more about average rates of change:
https://brainly.com/question/8728504
#SPJ1
Tonya spends 55% of her savings on a new dress. If she saved $120, how much was the dress?
Answers
Answer: The dress was $66
Step-by-step explanation:
55(120) divided by 100 and you'll get the price of the dress :)
Two concentric circles are shown. The length of the arc MN is 4π cm and the length of the arc RE is 8π cm.Which statements are correct? Select all that apply.ere to searchThe radius of the larger circle is 16 cm.The radius of the smaller circle is 16 cm.
Answers
We can express the length of an arc as a fraction of the circumference.
This fraction is equal to the the proportion between the measure of the arc and the full circle measure.
In this case, the measure is 45°, so the fraction should be:
[tex]\begin{gathered} \alpha=45\degree \\ \Rightarrow f=\frac{\alpha}{360\degree}=\frac{45\degree}{360\degree}=0.125 \end{gathered}[/tex]Then, we can express the arc MN as:
[tex]MN=C_1\cdot f[/tex]where C1 is the circumference of the smaller circle.
We can express then calculate it as:
[tex]\begin{gathered} MN=C_1\cdot f \\ C_1=\frac{MN}{f}=\frac{4\pi}{0.125}=32\pi \end{gathered}[/tex]As the circumference can be related to the radius, we can us this value to calcualte the radius of the smaller circle:
[tex]\begin{gathered} C_1=2\pi r_1 \\ r_1=\frac{C_1}{2\pi}=\frac{32\pi}{2\pi}=16 \end{gathered}[/tex]Then, the small circle has a radius of 16 cm and a circumference of 32π cm.
We can then calculate C2 and r2 for the bigger circle as:
[tex]\begin{gathered} RE=C_2\cdot f \\ C_2=\frac{RE}{f}=\frac{8\pi}{0.125}=64\pi \end{gathered}[/tex][tex]\begin{gathered} C_2=2\pi r_2 \\ r_2=\frac{C_2}{2\pi}=\frac{64\pi}{2\pi}=32 \end{gathered}[/tex]The bigger circle has a radius of 32 cm and a circumference of 64π cm.
We can now calculate the length of the segments NE and MR. Both are equal and can be calculated as the difference between the radius of the bigger circle (r2) and the radius of the smaller circle (r1):
[tex]NE=MR=r_2-r_1=32-16=16[/tex]Both segments, NE and MR, have a length of 16 cm.
We can now check the statements. The ones that are true are:
• The radius of the smaller circle is 16 cm.
,• The length of the segment MR is 16 cm.
,• The circumference of the larger circle is 64π cm.
Answer: The true statements are
• The radius of the smaller circle is 16 cm.
,• The length of the segment MR is 16 cm.
• The circumference of the larger circle is 64π cm.
Using the predicate symbols shown and appropriate quantifiers, write each English language statement asa predicate wff. (The domain is the whole world.)B(x): x is a ballR(x): x is roundS(x): x is a soccer ballc. All soccer balls are round.d. Some balls are not round.e. Some balls are round but soccer balls are not.f. Every round ball is a soccer ball.
Answers
c) The statement "All soccer balls are round" is equivalent to "For all x, if S(x) then R(x)" and it can be written in predicate wff as
[tex]\forall x\text{ (S(x)}\rightarrow R(x))[/tex]d) The statement "Some balls are not round" is equivalent to "There exist some x such that B(x) and not R(x)", which can be written in predicate wff as
[tex]\mathfrak{\Im }x(B(x)\wedge\urcorner R(x))[/tex]e) The statement "Some balls are round but soccer balls are not" is equivalent to "There exist x such that B(x) and R(x) and there exist x such that S(x) and not R(x)", can be written in prediacte wff as
[tex]\mathfrak{\Im }x(B(x)\wedge R(x))\wedge\mathfrak{\Im }x(S(x)\wedge\urcorner R(x))[/tex]f) The statement "Every round ball is a soccer ball" is equivalent to "For all x, if R(x) then S(x)", can be written in prediacte wff as
[tex]\forall x(R(x)\rightarrow S(x))[/tex]
You deposited $3,000 in the bank in 2019. It is compounded annually at 4%. How much money will you have in 9 years (in 2028)?
Answers
ANSWER
[tex]\begin{equation*} \$4,269.94 \end{equation*}[/tex]EXPLANATION
To find the amount of money that you will have in 9 years, apply the formula for annually compounded amount:
[tex]A=P(1+r)^t[/tex]where P = principal
r = interest rate
t = number of years
Hence, the amount after 9 years is:
[tex]\begin{gathered} A=3000(1+\frac{4}{100})^9 \\ A=3000(1+0.04)^9=3000(1.04)^9 \\ A=\$4,269.94 \end{gathered}[/tex]That is the answer.