# How do you find the exact values of costheta and sintheta when tantheta=5/12?

Nov 7, 2016

sinθ=$\frac{5}{13}$

and cosθ=$\frac{12}{13}$

#### Explanation:

Draw a right triangle with base 12 and height 5 units with angle $\theta$ sitting on the base as shown below

Apply Pythagoras theorem to get hypotenuse= 13 units

Work out sin$\theta = \frac{5}{13}$

and cos$\theta = \frac{12}{13}$

Nov 7, 2016

$\cos \theta = \frac{12}{13}$ and $\sin \theta = \frac{5}{13}$
If $\tan \theta = \frac{5}{12} = \frac{o p p o s i t e s i \mathrm{de}}{a \mathrm{dj} a c e n t s i \mathrm{de}}$
So the hypotenuse $= \sqrt{{5}^{2} + {12}^{2}} = \sqrt{169} = 13$
$\cos \theta =$(adjacent side)/(hypotenuse)$= \frac{12}{13}$
$\sin \theta =$(opposite side)/(hypotenuse)$= \frac{5}{13}$