81.5k views
4 votes
Find the following trigonometric values.

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

User VMois
by
6.7k points

2 Answers

4 votes

Final answer:

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

User Stefan Lasiewski
by
6.2k points
4 votes

Answer:


(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) )

----------------------------------------------------------

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

User Jaspreet Jolly
by
5.8k points
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