Question

Find the following trigonometric values.

Express your answers exactly.
COS
cos (7pie/4)=
sin (7pie/4)=

Answer 1

The value of cos (7π/4) is -√2/2, and the value of sin (7π/4) is -√2/2.

Step-by-step explanation:

To find the value of cos (7π/4) and sin (7π/4), we can use the unit circle. In the unit circle, the angle 7π/4 is in the third quadrant. The cosine value in the third quadrant is negative, and the sine value is also negative.

Therefore, cos (7π/4) = -√2/2 and sin (7π/4) = -√2/2

Answer 2

`(1)/(√(2) )` and -
`(1)/(√(2) )`

Step-by-step explanation:

Note that
`(7\pi )/(4)` is in the fourth quadrant where

cos > 0 and sin < 0

cos(
`(7\pi )/(4)` ) = cos (2π -
`(7\pi )/(4)` ) = cos(
`(\pi )/(4)` ) =
`(1)/(√(2) )`

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sin (
`(7\pi )/(4)` ) = - sin(
`(\pi )/(4)` ) = -
`(1)/(√(2) )`