Mathematics

Problem

Answer the following questions related to trigonometric functions. a. (i) State the fundamental Pythagorean identity involving

\sin \theta

and

\cos \theta

. b. (ii) Determine, with reasons, the signs (positive or negative) of

\sin \theta

and

\cos \theta

when

\theta

lies in the third quadrant. c. (iii) An angle

\theta

is such that

\sin \theta = -\dfrac{4}{5}

and

\theta

lies in the third quadrant. Find the corresponding value of

\cos \theta

. Show your working clearly.