Precalculus Review

Radian and right triangles

Radian. We will consider a circle of radius

, and call it the unit circle. Then an arc length

of the unit circle is called a radian, typically denoted by $\theta$ . Recall that the circumference of the unit circle is $2 \pi$ . For example, $\angle AOB = 30^\circ$ , $45^\circ$ and $360^\circ$ are equal to $\theta = \dfrac{ \pi }{6}$ , $\dfrac{ \pi }{4}$ and $2 \pi$ .

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Special right triangles. If a right triangle has its adjacent side and opposite side , then it must have the hypotenuse $\sqrt{2}$ and the angle ${\theta = \dfrac{ \pi }{4}}$ .

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Similarly the right triangle with opposite side and hypotenuse determines the adjacent side $\sqrt{3}$ and the angle ${\theta = \dfrac{ \pi }{6}}$ .