How do you find the amplitude and period of y=sin(-5x)?

Jul 9, 2015

$a = 2 , T = \frac{2}{5} \pi$

Explanation:

$f \left(x\right) = A \sin \left(B x + C\right)$ or $g \left(x\right) = A \cos \left(B x + C\right)$

Repair that $- 1 \le \sin u \le 1$

Then $- A \le A \sin u \le A$

Amplitude $a = A - \left(- A\right) = 2 A$

For period, repair that $\sin \left(u + 2 k \pi\right) = \sin u = \sin \left(- u\right)$

$B {x}_{0} + C = 0 \setminus R i g h t a r r o w {x}_{0} = - \frac{C}{B}$

$B {x}_{1} + C = 2 \pi \setminus R i g h t a r r o w {x}_{1} = \frac{2 \pi - C}{B}$

Period $T = {x}_{1} - {x}_{0} = \frac{2 \pi - C}{B} + \frac{C}{B} = \frac{2 \pi}{B}$

In your case, $A = 1 , B = 5 , C = 0$