Find the exact values of the following trigonometric ratios

MATHEMATICS · Multi-part · A Level · Mathematics · Trigonometry · Trigonometry

Problem

Find the exact values of the following trigonometric ratios. Show each reduction step that brings the given angle into the interval

0\le x<2\pi

and state the final value obtained from the unit circle. (i)

\sin \left( \dfrac{13\pi}{6} \right)

(ii)

\cos \left( -\dfrac{7\pi}{4} \right)

(iii)

\tan \left( \dfrac{19\pi}{3} \right)

(iv)

\csc \left( -\dfrac{11\pi}{6} \right)

(v)

\sec \left( \dfrac{17\pi}{4} \right)