A student is comparing the two numbers and

MATHEMATICS · Subjective · CBSE · Mathematics · Trigonometric Functions · Trigonometric Functions

Problem

A student is comparing the two numbers

P=\sin170^{\circ}

and

Q=\cos10^{\circ}

. (i) State the fundamental Pythagorean identity relating

\sin\theta

and

\cos\theta

for any real angle

\theta

. (ii) Describe, with reasons based on the unit circle, the signs (positive or negative) of

\sin170^{\circ}

and

\cos10^{\circ}

. (iii) Without using tables or a calculator, decide which of the two numbers,

P

Q

, is larger. Give a clear logical justification for your answer.