Sine, cosine and tangent functions

Given a right triangle with acute angle $ \theta$, the sine, cosine and tangent functions of the radian $ \theta$ are respectively given by

$\displaystyle \sin\theta = \dfrac{ b }{c}; \hspace{0.2in} \cos\theta = \dfrac{ a }{c}; \hspace{0.2in} \tan\theta = \dfrac{ b }{a}.$ (1-1)

\includegraphics{lec09c.ps}

If the hypotenuse of right triangle is $ 1$, then (i) the opposite side equals $ \sin\theta$ and (ii) the adjacent side equals $ \cos\theta$. By Pythagorean theorem we obtain $ {(\sin\theta)^2 + (\cos\theta)^2 = 1}$, which we will write as

$\displaystyle \sin^2\theta + \cos^2\theta = 1
$

\includegraphics{lec09d.ps}

We can also see that

$\displaystyle \tan\theta = \dfrac{\sin\theta}{\cos\theta}.$ (1-2)



Department of Mathematics
Last modified: 2005-09-29