Identify the base trig function: sine, cosine, tangent, cotangent, secant, or cosecant
Use the standard period:
Sine: (2pi)
Cosine: (2pi)
Tangent: (pi)
Cotangent: (pi)
Secant: (2pi)
Cosecant: (2pi)
For (f(x)=asin(bx+c)), (f(x)=acos(bx+c)), (f(x)=asec(bx+c)), or (f(x)=acsc(bx+c)), use period (= frac{2pi}{|b|})
For (f(x)=atan(bx+c)) or (f(x)=acot(bx+c)), use period (= frac{pi}{|b|})
Ignore vertical shifts and amplitude when finding period
If the function is a sum of trig functions, find the period of each term
If the terms have different periods, use the least common multiple when it exists
If the function includes nested trig or transformations, rewrite it into standard form first
For expressions with degrees, use:
Sine, cosine, secant, cosecant: period (= frac{360^circ}{|b|})
Tangent, cotangent: period (= frac{180^circ}{|b|})
Check whether the function repeats after the smallest positive interval
Verify by comparing (f(x)) and (f(x+T)) for the candidate period (T)