Question

How do you find the exact functional value cos(285 degrees) using the cosine sum or difference identity?

Answer 1

Find cos (285) deg

Ans: `(sqrt2/4)(sqrt3 - 1)`

Explanation:

cos (285) = cos (135 + 150)
Apply the trig identity: cos (a + b) = cos a.cos b - sin a.sin b
Use the Trig Table of Special Arcs.
Call a = 135 --> `sin a = sqrt2/2` and `cos a = -sqrt2/2`
Cal b = 150 --> `sin b = 1/2` and `cos b = -sqrt3/2.`
We get:
`cos (285) = ((sqrt2)(sqrt3))/4 - sqrt2/4 = sqrt2/4(sqrt3 - 1)`

Check by calculator:
cos 285 = 0.26
`(sqrt2/4)(sqrt3 - 1) = ((0.73)(1.41))/4 = 0.26.` OK