Question

Determine the period of the following trigonometric function.
y, equals, one half, sine, left parenthesis, start fraction, 6, x, divided by, 7, end fraction, minus, start fraction, 3, pi, divided by, 2, end fraction, right parenthesis, minus, 3
y=
2
1
​
sin(
7
6x
​
−
2
3π
​
)−3

Answer 1

The argument of the sine is (6/7)x − 3π/2, so the angular frequency is b = 6/7. The period is 2π/|b| = 2π/(6/7) = 7π/3.

(Phase shift and vertical shift do not change the period.)