# Using sketch to find exact value of trigonometric expression

Use sketch to find exact value of $\tan (\cos^{-1}\dfrac{5}{13})$

I drew a right triangle with angle $\theta$ and sides $12,5,3.$
If $\cos \theta=\frac{5}{13},$ then $\sin \theta = \frac{12}{13}$ and $\tan \theta = \frac{12}{5}.$

This isn't correct since tangent is greater than one. How would I solve this correctly? (Please show steps) Thanks.

• No, it's correct, tangent can be greater than one. – agha Aug 4 '14 at 21:18
• to see why $\tan\theta$ can be greater than zero, use a sketch. – John Joy Oct 5 '14 at 19:36

Print it and give it to your teacher. Or send him this link. Answer is $\pm\frac{12}{5}=\pm 2.4$
There's no reason that $\tan \theta$ needs to be less than $1$. You're likely able to check for yourself that $\tan(\pi/3) = \sqrt 3$ (or $\tan(60^\circ)$ if you prefer degrees to radians).