Radian and right triangles

Radian. We will consider a circle of radius $ 1$, and call it the unit circle. Then an arc length $ AB$ 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. The right triangle with adjacent side $ 1$ and opposite side $ 1$ gives the hypotenuse $ \sqrt{2}$ and the angle  $ {\theta = \dfrac{ \pi }{4}}$.

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The right triangle with opposite side $ 1$ and hypotenuse $ 2$ gives the adjacent side $ \sqrt{3}$ and the angle  $ {\theta = \dfrac{ \pi }{6}}$.



Department of Mathematics
Last modified: 2005-09-29