1 of 8 0-day streak

Use exact trigonometric identities and quadrant information

Question 1 of 8

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Consider an angle \(\theta\) in QII

\sin\theta=\frac{33}{65}

Use exact trigonometric relationships to find \(\cos\theta\)

(a)1 mark

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

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

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

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

\sin\theta+\cos\theta=1

(b)1 mark

Which equality correctly isolates the square of the other ratio?

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

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

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

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

\(\cos^2\theta\)

(d)1 mark

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

Take the negative square root

Take the positive square root

(e)1 mark

Calculate \(\cos\theta\), keeping the sign required by the quadrant

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

\(\cos\theta\)