Solve the following quadratic trig equations algebraically (without graphing technology) for the domain 0 ≤ x ≤ 360°. Use exact solutions whenever possible.
1. 6cos^2(θ) + cos(θ) - 1 = 0
2. 2 - 2sin^2(θ) = cos(θ)
Thanks for your help

Question

Solve the following quadratic trig equations algebraically (without graphing technology) for the domain 0 ≤ x ≤ 360°. Use exact solutions whenever possible.
1. 6cos^2(θ) + cos(θ) - 1 = 0
2. 2 - 2sin^2(θ) = cos(θ)
Thanks for your help

tkhunny · Answer

What's preventing you from solving these?

For the first, simply factor.  $(2\cos(\theta) + 1)(3\cos(\theta) - 1) = 0$.  You could have done that!

For the second, use the Pythagorean identity to convert the sine to cosine and it will be very similar to the first.