Question

How do you find the exact value of cos 7pi/4?

Answer 1

`cos(5.49778714377)=0.70710678117`.

Explanation:

Evaluate `7xxpi` then divide that by `4` first
So `7xxpi` is `7xxpi` or `21.9911485751`

`7xxpi=21.9911485751`

Now divide `7xxpi` by `4`

`21.9911485751/4=5.49778714377`

That means `cos (7)(pi)/4` is `cos(5.49778714377)`

`cos(5.49778714377)=0.70710678117`.

Answer 2

First, convert to degrees (for many people, these are more convenient to work with).

Explanation:

The conversion factor between radians and degrees is `180/pi`

`(7pi)/4 xx 180/pi`

`=315^@`

Now, this is a special angle, which can be found by using the special triangles.

But first, we must determine the reference angle of `315^@`. The reference angle `beta` of any positive angle `theta` is within the interval `0^@ <= beta < 90^@`, linking the terminal side of `theta` to the x axis. The closest intersection with the x axis for `315^@` would be at `360^@`: `360^@ - 315^@ = 45^@`. Our reference angle is `45^@`.

We now know that we must use the `45-45-90; 1, 1 sqrt(2)` triangle, as shown in the following graphic.

Now, it's just a matter of applying the definition of cos to find the wanted trig ratio.

`cos =` adjacent/hypotenuse

`cos = 1/sqrt(2)`, or `0.707`, as a fellow contributor stated. However, for the purpose of this problem, I think your teacher would be looking for an exact value answer: `cos((7pi)/4) = 1/sqrt(2)`

Hopefully this helps!

Answer 3

`sqrt2/2`

Explanation:

Trig unit circle and trig table -->
`cos ((7pi)/4) = cos (-pi/4 + (8pi)/4) = cos (-pi/4 + 2pi) =`
`cos (-pi/4) = cos (pi/4) = sqrt2/2`