Using sketch to find exact value of trigonometric expression

$\begingroup$

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.

$\endgroup$ 2

2 Answers

$\begingroup$

Print it and give it to your teacher. Or send him this link. Answer is $\pm\frac{12}{5}=\pm 2.4$

$\endgroup$ $\begingroup$

Nope, you're right.

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).

$\endgroup$

Your Answer

Sign up or log in

Sign up using Google Sign up using Facebook Sign up using Email and Password Submit

Post as a guest

Post Your Answer Discard

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy