Evaluate. Show all steps in the simplification process. Express answers in lowest terms.
(No decimal answers).
a. csc 150° sin 210° + 3 cos^2(135°)
a. csc 150° sin 210° + 3 cos^2(135°)
First, let's find the exact values of the trigonometric functions at the given angles:
csc 150° = 1/sin 150° = 1/(-1/2) = -2
sin 210° = -1/2
cos 135° = -√2/2
Now substitute these values into the expression:
-2*(-1/2) + 3 * (-√2/2)^2
= 1 + 3 * (2/4)
= 1 + 3/2
= 2.5
Therefore, csc 150° sin 210° + 3 cos^2(135°) = 2.5.