Unit T Big Question # 1

How do the trig graphs relate to the Unit circle?
a) Period

Sine
Sine is positive in the first and third quadrant and negative in the third and forth. Sine needs to go once around the unit circle for the cycle to repeat, which is 2pi.

Cosine
Cosine is positive in the first and forth quadrant, and negative in the second and the third. like sine, cosine needs to go around the unit circle once for the cycle to repeat, which would be 2pi.

Tangent
Tangent is positive in the first and third quadrant and negative in the second and forth. Unlike sine and cosine, tangent needs to go half way around the unit circle for the cycle to repeat, which is pi.

b) Amplitude

Sine and cosine have amplitudes because both of them have a spot on the unit circle. While tangent and cotangent doesn't because it's value is y/x or sin/cos. Secant and cosecant are the reciprocals of sine and cosine and because secant is 1/sine it could be undefined because sine equals zero at 0 and pi.