Answer to Question #206419 in Trigonometry for Elissa

Question

By drawing a relevant triangle,prove that

 

tan θ = sin θ / cos θ

and

cos^2 θ + sin^2 θ = 1

Answer 1

Consider the right-angled triangle ABC, with AB=1, C = 90° and A= θ°.

$\sin \theta =\frac{BC}{AB}=\frac{BC}{1}=BC$

$\cos \theta =\frac{AC}{AB}=\frac{AC}{1}=AC$

$\tan \theta =\frac{BC}{AC}=\frac{\sin \theta}{\cos \theta}$

Pythagorean theorem: $1=AC^2+BC^2=\cos ^2\theta +\sin^2\theta$