Use exact trigonometric identities and quadrant information practice questions | Mathematical Methods (Year 12, VCE Units 3 & 4, Solving equations, Circular functions and exact values)

(a)1 mark

Which identity gives a valid plan for finding the other ratios?

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

Then use the stated quadrant to choose the signs of the ratios

\sin\theta+\cos\theta=1

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

(b)1 mark

Which equality correctly isolates the square of the other ratio?

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

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

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

(c)1 mark

Find \(\sin^2\theta\) exactly

\(\sin^2\theta\)

(d)1 mark

Which sign should be used for the square root in \(\sin\theta\)?

Take the positive square root

Take the negative square root

(e)4 marks

Find \(\sin\theta\) exactly

For a surd, use the labelled form \(\frac{P+Q\sqrt{R}}{S}\) and enter its coefficients

\(P_{\sin\theta}\) \(Q_{\sin\theta}\) \(R_{\sin\theta}\) \(S_{\sin\theta}\)