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5.04 Trigonometric identities

Interactive practice questions

Which of the following options correctly completes the identity?

$\tan z=\editable{}$tanz=

$\cot z$cotz

A

$\frac{\cos z}{\sin z}$coszsinz

B

$\frac{\sin z}{\cos z}$sinzcosz

C

$\frac{1}{\cot x}$1cotx

D
Easy
< 1min

Given that $\sin x=\frac{4}{5}$sinx=45 and $\cos x=\frac{3}{5}$cosx=35, find $\tan x$tanx.

Easy
< 1min

Use properties of the trigonometric functions to find the exact value of $\tan10^\circ-\frac{\sin10^\circ}{\cos10^\circ}$tan10°sin10°cos10°

Easy
< 1min

Given that $\cos x=\frac{15}{17}$cosx=1517 and $\tan x=\frac{8}{15}$tanx=815, find $\sin x$sinx.

Easy
1min
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Outcomes

MA11-1

uses algebraic and graphical techniques to solve, and where appropriate, compare alternative solutions to problems

MA11-4

uses the concepts and techniques of periodic functions in the solutions of trigonometric equations or proof of trigonometric identities

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