Question

Help please?
Determine the number of cycles each trigonometric function has in the interval from 0 to 2π. Find the amplitude and period of each function.

a. y = sin5θ
b. y = -5sin2πθ
c. y = 2cos4θ
d. y = 4cos2θ

Answer 1

in general sin and cos can be written

\[y = acos(bx)...... or ..... y = asin(bx)\]

a is the amplitude of the function.

e.g. y = 3sin(x) has an amplitude of 3

y = -2cos(x) has an amplitude of 2 and the curve has been reversed.

the period is found using

\[period = \frac{2\pi}{\left| b \right|}\]

so for y = cos(5x) the period or length of the cycle is

\[\frac{2\pi}{5}\]

hope this helps