IBHardGeometry & Trigonometry10–12

Solving a Trigonometric Equation Over a Full Turn

Resolver uma Equação Trigonométrica numa Volta Completa

Solve $2\sin^{2} x = 1 + \cos x$ for $0 \le x \le 2\pi$ .

Two different trigonometric functions appear, so use the Pythagorean identity to express everything through one of them. What is left is a quadratic in that function, and each of its roots may give more than one angle in the interval.

Solution

Step 1 of 11

1.Replace $\sin^{2} x$ with $1 - \cos^{2} x$ :