Tangent Function Periodicity Identity
This video introduces the periodicity identities for the tangent function. Essentially, this looks at what happens when the angle is shifted pi/2 radians or 90 degrees,
The general strategy is to start with a ray on the unit circle that has an angle theta. The ray and angle are then shifted by 90 degrees or pi/2 radians. Basically, the right triangle formed originally is shifted by 90 degrees, but still has the same values for its two legs. These values can then be compared to the (x, y) coordinate of the shifted ray.
The tangent function is equal to the ratio of the sine function to the cosine function. Using the identities for sine and cosine with pi/2 radians added to the angle theta, it can be shown that the tangent at this new angle is equal to the opposite of the cotangent function at the original angle, theta.
Khan Academy exercise to practice:
1. Trig Identities from Reflection and Rotation: https://www.khanacademy.org/math/trig...
EulersAcademy.org