Question

Determine the period of the following tangent function.
y, equals, minus, 8, tan, left parenthesis, start fraction, 4, x, divided by, 3, end fraction, minus, start fraction, pi, divided by, 2, end fraction, right parenthesis, minus, 1
y=−8tan(
3
4x
​
−
2
π
​
)−1

Answer 1

The basic tangent has period π. For y = −8 tan((4/3)x − π/2) − 1 the horizontal stretch factor is 4/3, so the period is

period = π / (4/3) = 3π/4.

(The −8 and the −1 do not affect the period.)