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The Unit Circle and Radian Measure

Radian Measure Arc Length and Sector Area worksheet and textbook only The Unit Circle worksheet and textbook only Multiples of

$\frac{\pi}{6}$ and

$\frac{\pi}{4}$ Pythagorean Identity

Extension Problems

Fill in the blanks so that the multiplication of the rows and columns are correct.

$\frac{5\pi}{6}$	$\times$	$\frac{2\pi}{3}$	$\times$	$0$	$=1$
$\times$		$\times$		$\times$
$\frac{\pi}{6}$	$\times$	$\sin{\frac{\pi}{4}}$	$\times$	$\frac{3\pi}{4}$	$=-\frac{1}{4}$
$\times$		$\times$		$\times$
$\frac{5\pi}{6}$	$\times$	$\frac{\pi}{2}$	$\times$	$\frac{3\pi}{4}$	$=0$
$\parallel$		$\parallel$		$\parallel$
$\frac{1}{4}$		$0$		$-\frac{1}{2}$

Evaluate:

a) $\displaystyle\sin{\left(\frac{\pi}{2}-\theta\right)}+\sin{\left(\pi-\theta\right)}-\cos{\left(\frac{\pi}{2}-\theta\right)}+\cos{\left(\pi-\theta\right)}$

b) $\displaystyle\frac{1-\sin{\left(\pi-\theta\right)}}{1+\sin{\left(\frac{\pi}{2}-\theta\right)}}\times\frac{1-\cos{\left(\pi-\theta\right)}}{1-\cos{\left(\frac{\pi}{2}-\theta\right)}}$

Simplify the following to a single fraction:
$\displaystyle\frac{1-\sin{x}-\cos{x}}{1-\sin{x}+\cos{x}}+\frac{1+\sin{x}+\cos{x}}{1+\sin{x}-\cos{x}}$

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Extension Problems

The Unit Circle and Radian Measure