Question

How do you use the angle sum identity to find the exact value of cos 195?

Answer 1

`Use` `the` `trig` `identity` `:` `cos (a + b)` `= cos a*cos b - sin a*sin b.`
`cos 195^circ = cos (180 + 15) = cos 180*cos 15 - sin 180* sin 15`
#= (-1)*(sqrt3)/2 - 0 = -(sqrt3)/2 #
`cos 195^circ = - (sqrt3)/2`

Answer 2

Find two special angles that add up to `195^@`

`(30+ 165)^@`. -- no`165^@` is not a special angle

`(45+150)^@`. Yes that will work.

(So would `(60+135)^@`)

`cos195^@ = cos(45^@ + 150^@)`

Now use the formula and the sine and cosine of the special angles.