trig problem, step by step

Question

Solve for all solutions =

Answer 1

Hi Chlo A.,

Having a graphing calculator will help to visualize the problem. I plugged the two equations into my TI-89 and saw four intersections for 0 ≤ θ < 2π.

We can solve this by solving for θ:

7cos(2θ) = 7sin²(θ) + 5

cos(2θ) = [1 - cos(2θ)]/2 + 5/7

2cos(2θ) = 1 - cos(2θ) + 10/7

3cos(2θ) = 17/7

cos(2θ) = 17/21

2θ = cos^-1(17/21)

θ = [cos^-1(17/21)]/2

θ = 0.314 radians

For 0 ≤ θ < 2π, and referring to the graph, we have intersections at:

θ = 0.314 radians

θ = π - 0.314 = 2.83 radians

θ = π + 0.314 = 3.46 radians

θ = 2π - 0.314 = 5.97 radians

I hope this helps, Joe.

Answer 2

I agree with Doug C., but if you mean:

7cos 2x = 7 sin²x + 5 (where I wrote x instead of theta)

then cos 2x = 1 - 2 sin²x converts this to an equation in sin².