Exploring Trig Identities for AP Calculus

To solve them faster during exams

To understand their historical context

To create new identities during tests

To avoid learning them at all

sin(theta) * cos(theta) = 1

sin^2(theta) + cos^2(theta) = 1

tan(theta) + cot(theta) = 1

sec(theta) * csc(theta) = 1

sin(theta) * cos(theta) = 1

sin^2(theta) + cos^2(theta) = 1

tan(theta) + cot(theta) = 1

sec(theta) * csc(theta) = 1

Through integration of sine functions

Using the distance formula on the unit circle

By subtracting one cosine function from another

By differentiating the tangent function

cos(u-v) = sin(u) * cos(v) + cos(u) * sin(v)

cos(u-v) = sin(u) * sin(v) - cos(u) * cos(v)

cos(u-v) = cos(u) * cos(v) + sin(u) * sin(v)

cos(u-v) = cos(u) * cos(v) - sin(u) * sin(v)

Periodicity

Even and odd nature

Amplitude adjustments

Phase shifts

cos(u+v) = sin(u) * sin(v) - cos(u) * cos(v)

cos(u+v) = cos(u) * cos(v) + sin(u) * sin(v)

cos(u+v) = cos(u) * cos(v) - sin(u) * sin(v)

cos(u+v) = sin(u) * cos(v) + cos(u) * sin(v)

sin(theta) = cos(pi/2 - theta)

cos(theta) = sin(pi/2 + theta)

cos(theta) = cos(pi/2 - theta)

sin(theta) = sin(pi/2 - theta)

sin(u+v) = sin(u) * cos(v) + cos(u) * sin(v)

sin(u+v) = sin(u) * sin(v) - cos(u) * cos(v)

sin(u+v) = cos(u) * cos(v) + sin(u) * sin(v)

sin(u+v) = cos(u) * cos(v) - sin(u) * sin(v)

Even and odd identities

Cofunction identities

Sum and difference identities

Pythagorean identity