13D

Trigonometric graphs in radians

The graphs of sin, cos and tan in radians, amplitude, period, and the odd and even symmetry of the trig functions.

Amplitude and period

y = a sin bx and y = a cos bx

Orange: y = a sin bx. Blue dashed: y = a cos bx. a stretches vertically; b squeezes horizontally.

Try this

What value of $b$ gives period $\pi$?

Example 1●

State the amplitude and period of $y = 3\sin 2x$, and of $y = \cos\tfrac{x}{2}$.

$y = 3\sin 2x$: amplitude $3$, period $\dfrac{2\pi}{2} = \pi$.

$y = \cos\tfrac{x}{2}$: amplitude $1$, period $\dfrac{2\pi}{1/2} = 4\pi$.

Example 2●●

Find the range of $y = 2\cos x + 1$.

$\cos x$ ranges from $-1$ to $1$, so $2\cos x + 1$ ranges from $-1$ to $3$.

Flashcards

Amplitude of $asin bx$

$|a|$

Period of $asin bx$

$\dfrac{2\pi}{b}$

Period of $ an bx$

$\dfrac{\pi}{b}$

Odd trig functions

$\sin$ and $\tan$

Even trig function

$\cos$

Practice