Mathematics

Problem

Answer the following questions related to the trigonometric ratios of an acute angle

\theta

of a right triangle. a. (i) State the relationship between

\sin^2 \theta

and

\cos^2 \theta

. b. (ii) Explain, with reason, why the values of

\sin 45^\circ

and

\cos 45^\circ

are equal. c. (iii) If

\sin 45^\circ = \dfrac{\sqrt{2}}{2}

, verify the relationship stated in part (i) for

\theta = 45^\circ