New Zealand
Level 7 - NCEA Level 2

# Tangent Ratios (proofs and equivalences)

## Interactive practice questions

By finding the ratio represented by $\sin\theta$sinθ, $\cos\theta$cosθ and $\tan\theta$tanθ in the given figure, we want to prove that $\frac{\sin\theta}{\cos\theta}=\tan\theta$sinθcosθ=tanθ.

a

Write down the expression for $\sin\theta$sinθ.

b

Write down the expression for $\cos\theta$cosθ.

c

Hence, form an expression for $\frac{\sin\theta}{\cos\theta}$sinθcosθ.

d

Write down the expression for $\tan\theta$tanθ.

e

Does $\frac{\sin\theta}{\cos\theta}=\tan\theta$sinθcosθ=tanθ?

Yes

A

No

B

Yes

A

No

B
Easy
Approx 2 minutes
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### Outcomes

#### M7-4

Apply trigonometric relationships, including the sine and cosine rules, in two and three dimensions