Two angles and satisfy with in the third quadrant and with in the first quadrant.

MATHEMATICS · Multi-part · CBSE · Mathematics · Trigonometric Functions · Trigonometric Functions

Problem

Two angles

\alpha

and

\beta

satisfy

\sin\alpha=-\dfrac{5}{13}

with

\alpha

in the third quadrant and

\cos\beta=\dfrac45

with

\beta

in the first quadrant. (i) Find

\cos\alpha

and

\sin\beta

. (ii) For each angle, verify that

\sin^{2}+\cos^{2}=1

holds true with the values obtained.