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AustraliaVIC
VCE 12 Methods 2023

3.05 Trigonometric equations

Interactive practice questions

Consider the equation $-6\sin^{-1}x=\pi$6sin1x=π.

a

Solve the equation for $\sin^{-1}x$sin1x.

b

Consider your answer from part a. Does the equation have a solution?

Not enough information

A

Yes

B

No

C
c

Solve $\sin^{-1}x=-\frac{\pi}{6}$sin1x=π6 for $x$x.

Easy
4min

Consider the equation $4\tan^{-1}x=-3\pi$4tan1x=3π.

Easy
1min

Consider the equation $5\cos^{-1}\left(\frac{x}{3}-\frac{\pi}{3}\right)=5\pi$5cos1(x3π3)=5π.

Easy
5min

Consider the equation $\sin^{-1}x-\tan^{-1}1=-\frac{\pi}{4}$sin1xtan11=π4.

Easy
2min
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Outcomes

U34.AoS2.4

solution of equations of the form f(x) = g(x) over a specified interval, where f and g are functions of the type specified in the ‘Functions, relations and graphs’ area of study, by graphical, numerical and algebraic methods, as applicable

U34.AoS2.11

apply algebraic, logarithmic and circular function properties to the simplification of expressions and the solution of equations

U34.AoS2.10

solve by hand equations of the form sin(ax+b)=c, cos(ax+b)=c and tan(ax+b)=c with exact value solutions over a given interval

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