Mathematics

Problem

Answer the following questions related to the constant nature of certain trigonometric combinations. a. (i) Without substituting any numerical values, explain why

\sin^2 \theta + \cos^2 \theta = 1

for every acute angle

\theta

in a right-angled triangle. b. (ii) Using your reasoning from part (i), state whether

(\sin^2 30^\circ + \cos^2 60^\circ)

is equal to, less than, or greater than 1. Give a brief justification. c. (iii) Calculate the exact numerical value of

(\sin^2 30^\circ + \cos^2 60^\circ)

to confirm your answer in part (ii).

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