Let be an angle for which and lies in the third quadrant.

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

Problem

Let

\beta

be an angle for which

\cos\beta=-\dfrac{5}{13}

and

\beta

lies in the third quadrant. (a) Determine

\sin\beta

without using a calculator. (b) Find the value of

\tan\beta

in simplest form. (c) Evaluate the expression

S=\sin\beta+\cos\beta+\tan\beta

, giving your answer as a single simplified fraction.