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\theta+\cos\theta=1

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

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

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

(b)1 mark

Which equality correctly isolates the square of the other ratio?

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

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

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

Deduce \(\sin\theta\) from the given ratio and the stated quadrant

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

\(\sin\theta\)