Solve the trigonometric equation.

Question

Solve trigonometric equation on 0º≤x<360º and express answer in degrees to two decimal places.

4cos²x+5cosx-6=0

Please and thank you!

Answer 1

4cos^2x+5cosx-6=0

factor

(cosx+2)(4cosx-3)=0

cosx+2=0

cosx=-2 no solution

4cosx-3=0

4cosx=3

cosx=3/4=0.75

using arcos function

x=41.40962211º or 41º 24' 34.64"

x=41.41º