Trigonometric Identities

NZ Level 8 (NZC) Level 3 (NCEA) [In development]

Tangent Ratios (proofs and equivalences)

By finding the ratio represented by $\sin\theta$`s``i``n``θ`, $\cos\theta$`c``o``s``θ` and $\tan\theta$`t``a``n``θ` in the given figure, we want to prove that $\frac{\sin\theta}{\cos\theta}=\tan\theta$`s``i``n``θ``c``o``s``θ`=`t``a``n``θ`.

a

Write down the expression for $\sin\theta$`s``i``n``θ`.

b

Write down the expression for $\cos\theta$`c``o``s``θ`.

c

Hence, form an expression for $\frac{\sin\theta}{\cos\theta}$`s``i``n``θ``c``o``s``θ`.

d

Write down the expression for $\tan\theta$`t``a``n``θ`.

e

Does $\frac{\sin\theta}{\cos\theta}=\tan\theta$`s``i``n``θ``c``o``s``θ`=`t``a``n``θ`?

Yes

A

No

B

Yes

A

No

B

Easy

Approx 2 minutes

Sign up to try all questions

Manipulate trigonometric expressions

Apply trigonometric methods in solving problems