Identify the trig function type: sine, cosine, tangent, cotangent, secant, or cosecant
Use the base period:
Sine and cosine: (2pi)
Tangent and cotangent: (pi)
Secant and cosecant: (2pi)
If the function is (f(x)=sin(bx)) or (f(x)=cos(bx)), period (=frac{2pi}{|b|})
If the function is (f(x)=tan(bx)) or (f(x)=cot(bx)), period (=frac{pi}{|b|})
If the function is (f(x)=sec(bx)) or (f(x)=csc(bx)), period (=frac{2pi}{|b|})
For (f(x)=sin(bx+c)), (f(x)=cos(bx+c)), (f(x)=tan(bx+c)), (f(x)=cot(bx+c)), (f(x)=sec(bx+c)), or (f(x)=csc(bx+c)), use the same period formulas with (|b|)
Ignore vertical shifts and horizontal shifts when finding period
Simplify the coefficient of (x) before applying the formula
For expressions with multiple trig terms, find the period of each term and determine the least common period if needed
Verify the result by checking when the function repeats its values exactly