what is the exact value of cos(7pi/8)

Answer:

cos ([tex]\frac{7\pi}{8}[/tex]) = [tex]-\frac{\sqrt{2+\sqrt{2}}}{2}[/tex]

Decimal value: −0.9238795325...

Step-by-step explanation:

Write,

cos [tex]\frac{7\pi}{8}[/tex] = cos [tex](\pi-\frac{\pi}{8})[/tex] = −cos [tex]\frac{\pi }{8}[/tex]

Now using half angle formula, cos(x) = 2 cos²([tex]\frac{\pi }{2}[/tex]) − 1, we can write cos [tex]\frac{\pi }{4}[/tex] = 2

cos²([tex]\frac{\pi }{8}[/tex]) − 1

This means [tex]\frac{1}{\sqrt{2}}[/tex] + 1 = 2 cos²([tex]\frac{\pi }{8}[/tex])

2 cos²([tex]\frac{\pi }{8}[/tex]) = [tex]\frac{\sqrt{2}+1}{\sqrt{2}}[/tex]

cos²([tex]\frac{\pi }{8}[/tex]) = [tex]\frac{\sqrt{2}+1}{2\sqrt{2}}[/tex]

cos([tex]\frac{\pi }{8}[/tex]) = [tex]\sqrt{\frac{\sqrt{2}+1}{2\sqrt{2}}}[/tex]

Simplify,

[tex]\sqrt{\frac{\sqrt{2}+1}{2\sqrt{2}}}[/tex] = [tex]\sqrt{\frac{2+\sqrt{2}}{4}[/tex] = [tex]\frac{\sqrt{2+\sqrt{2}}}{2}[/tex]

Hence,

cos ([tex]\frac{7\pi}{8}[/tex]) = −cos ([tex]\frac{\pi }{8}[/tex]) = [tex]-\frac{\sqrt{2+\sqrt{2}}}{2}[/tex]

The exact value of cos(7pi/8) is [tex]\rm -\dfrac{\sqrt{2+\sqrt{2}} }{2 }[/tex] and this can be determined by using the trigonometric properties.

Given :

Expression  -- [tex]\rm cos(\dfrac{7\pi}{8})[/tex]

The following steps can be used to determine the exact value of the given expression:

Step 1 - Write the given expression.

[tex]=\rm cos(\dfrac{7\pi}{8})[/tex]

Step 2 - Rewrite the above expression.

[tex]= \rm cos(\dfrac{8\pi - \pi}{8})[/tex]

Step 3 - The above expression is reduced to:

[tex]= \rm -cos(\dfrac{ \pi}{8})[/tex]    --- (1)

Step 4 - According to the trigonometric properties:

[tex]\rm cos(x) = 2 cos^2(\frac{x}{2})-1[/tex]

Step 5 - Substitute the value of x = [tex]\pi[/tex]/4 in the above expression.

[tex]\rm cos(\frac{\pi}{4}) = 2 cos^2(\frac{\pi}{8})-1[/tex]

Step 6 - Simplify the above expression.

[tex]\rm cos(\frac{\pi}{8})=\sqrt{\dfrac{\dfrac{1}{\sqrt{2}} +1}{2}}[/tex]

[tex]\rm cos(\frac{\pi}{8})=\sqrt{\dfrac{1+\sqrt{2} }{2\sqrt{2} }[/tex]

[tex]\rm cos(\frac{\pi}{8})=\dfrac{\sqrt{2+\sqrt{2}} }{2 }[/tex]

Step 7 - Substitute the value of cos([tex]\pi[/tex]/8) in the expression (1).

[tex]\rm -cos(\frac{\pi}{8})=-\dfrac{\sqrt{2+\sqrt{2}} }{2 }[/tex]

For more information, refer to the link given below:

https://brainly.com/question/17081568

Help pls this is timed!!!!!!! Pls and thank you ;P
Who supported the formation of Washington Territory out of a belief that it was America’s destiny to settle the Pacific Northwest?

A.)President Millard Fillmore
B.)Governor Isaac Stevens
C.)Oregon Territory’s northern settlers
D.)Oregon Territory’s southern settlers

If ya dont mind can u help me .....thanks


Today 108 people visited a water park during the first hour that the park was open.

This number of people is 40% of the number of people who visited the water park

during the first hour yesterday.




How many people visited the water park during the first hour yesterday?

F 148

G 270

H 292

J 151

What is the solution to the equation? 13 3/4+X= 7 1/ 4​

ratio of width to length is 2:3 if the length 18 meters what is the width

In ΔKLM, l = 820 cm, m = 560 cm and ∠K=169°. Find the length of k, to the nearest centimeter.

f(x) = 5x^2 + 14
g(x) = 4x + 8
What is f(g(-8))?

A pair of shoes usually sells for $60. If the shoes are 20% off, and sales tax is 7%, what is the total price of the shoes, including tax?

i need help can someone help me

Use complete sentences to describe why postulates are helpful.​

Write System of Equations from Context

Mason owns a trucking company. For every truck that goes out, Mason must pay the driver $13 per hour of driving and also has an expense of $1 per mile driven for gas and maintenance. On one particular day, the driver drove an average of 30 miles per hour and Mason's total expenses for the driver, gas and truck maintenance were $258. Write a system of equations that could be used to determine the number of hours the driver worked and the number of miles the truck drove. Define the variables that you use to write the system.

*PLEASE HELP ME ASAP* Sydnis room is 32 ft by 40 ft. She needs to make a scale drawing of her room that is 8 in. by 10 inc. What is the scale she needs to use?
1 inch = 8ft
1 inch = 4 ft
1 inch = 2 ft
1 inch = 1 ft

a triangle has sides measuring 31 in 18in and 25 in what is the perimeter of the triangle​

The Fun Guys game rental store charges an annual fee of $5 plus $5.50 per game

rented.

The Game Bank charges an annual fee of $11 plus $2.50 per game.

For how many game rentals will the cost be the same at both stores?

(Write an equation to go with the problem) Miranda goes to the store to buy 3 apples and some rice. The total was 6.50. If the rice cost $5.00, what was the cost per Apple?

Write the equation of a vertical line running through the point (-2,-10)

select all relations that are functions from the choices below.

The diagram shows a square with a perimeter of 20 cm.
Not drawn
accurately
Eight of these squares fit together to make a rectangle.
Not drawnaccurately
What is the perimeter of the rectangle?​

HELP!!!!!!!!!!!!!!!!!!!!

Please help! I could fail if I don’t get theese right

Two trains, Train A and Train B, weigh a total of 381 tons. Train A is heavier than Train B.
The difference of their weights is 193 tons. What is the weight of each train?
I need this answer quick!

Which postulate proves that the triangles below are similar?
SSS
AA
SAS
These triangles are not similar

38 < 4x - 10
help me out plz n ty

Plz help me I will give you brainliest and 10 points

Pls help I’m being timed

Olivia has a points card for a movie theater. She receives 80 rewards points just for signing up. She earns 2.5 points for each visit to the movie theater. She needs at least 105 points for a free movie ticket. Write and solve an inequality which can be used to determine xx, the number of visits Olivia can make to earn her first free movie ticket.

are 2x3 and 4x4 like or unlike terms

cos 2 * (x/2) = (sec(x) + 1)/(2sec(x))

Evaluate the expression 42 + 5/9y

I need help with this ​

When multiplying or dividing integers, if the signs are the same, you keep the sign for the answer.
GIVING BRAINLIST PLEASE ANSWER CORRECT!!! ‍
False

True