What is the period and amplitude for $cos (\frac{π}{5}) (x)$ $cos(pi/5)(x)$ ?

Question

6863 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-07-25T13:57:12

As below.

Standard form of cosine function is $y = A cos (B x - C) + D$ $y = A cos (Bx - C) + D$

Given $y = cos ((\frac{π}{5}) x)$ $y = cos ((pi/5) x)$

$A = 1, B = \frac{π}{5}, C = D = 0$ $A = 1, B = pi/5, C = D = 0$

Amplitude $= | A | = 1$ $= |A| = 1$

Period $= \frac{2 π}{| B |} = \frac{2 π}{\frac{π}{5}} = 10$ $= (2 pi) / |B| = (2pi) / (pi/5) = 10$

Phase Shift $= - \frac{C}{B} = 0$ $= -C / B = 0$

Vertical Shift $= D = 0$ $= D = 0$

graph{cos ((pi/5) x) [-10, 10, -5, 5]}

What is the period and amplitude for cos(π5)(x)cos(pi/5)(x)?