1 of 8 0-day streak

Use exact trigonometric identities and quadrant information

Question 1 of 8

No calculator

The angle \(\theta\) is in QI

\sin\theta=\frac{15}{17}

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

(a)1 mark

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

\sin\theta+\cos\theta=1

\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

(b)1 mark

Which equality correctly isolates the square of the other ratio?

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

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

\cos\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

Find \(\cos\theta\) exactly

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

\(\cos\theta\)