State the amplitude of the following functions:
a) y = cos theta
b) y = 1/2cos theta
c) y = -2cos theta
To find the amplitude of a trigonometric function, you need to examine the coefficient in front of the trigonometric function.
a) For the function y = cos(theta), there is no coefficient in front of the cos function. In this case, the coefficient is understood to be 1. Therefore, the amplitude is 1.
b) For the function y = (1/2)cos(theta), the coefficient in front of the cos function is 1/2. Therefore, the amplitude is 1/2.
c) For the function y = -2cos(theta), the coefficient in front of the cos function is -2. Therefore, the amplitude is 2.
In general, the amplitude of a cosine function y = Acos(theta) is equal to the absolute value of A.