Review 5.3 Solving Trigonometric Equations

Summary:
• To solve a trigonometric equation by using standard algebraic techniques.
• Solving trigonometric equations of quadratic type.
• Solving trigonometric equations involving multiple angles.
• Use inverse function to solve the trigonometric equations.


Rules for solving trigonometric equation:
• Algebra rule (factor, simplify, combine terms).
• Constantly be aware of to the interval for each problem.
• For inverse functions, try to use several different identities to work out the problem.
• Do not forget to add 2nπ for general solution of sine and cosine; add n π for general solution of tangent.


Example 1: Solve 2sin²x+3cosx-3=0
Try to rewriting the equation so that it has only cosine functions.
2sin²x+3cosx-3=0
2（1-cos²x）+3cosx-3=0 Pythagorean identity
Setting each factor equal to zero, to get the general solution:
2cos²x-3cosx+1=0 Multiply both sides by-1
(2cosx-1)(cos x-1)=0 Factor
cos x=1/2 and cos x=1
x=2nπ，x=π/3+2nπ，x=5π/3+2nπ