CAIE A-Level Mathematics AS 1.5.3 Inverse Trig Notation Questions

Practise interpreting sin^-1, cos^-1 and tan^-1 as principal inverse values when solving equations or finding exact constants.

Exam points

Interpret sin⁻¹x, cos⁻¹x and tan⁻¹x as principal values of the inverse trigonometric functions.
Solve equations involving inverse trigonometric notation by isolating the inverse value and applying the corresponding trigonometric function, respecting the principal value.

[Maximum number: 2]

Find the exact value of t that satisfies the equation

3 \sin ^{-1}(3 t)+2 \cos ^{-1}\left(\frac{1}{2} \sqrt{2}\right)=\pi .

Figure for Question CAIE A-Level Mathematics AS 1.5.3 Inverse Trig Notation Questions question 1 — CAIE A-Level Mathematics AS

Solve at least as far as $\sin ^{-1} 3 t=k \pi$ with correct value for $\cos ^{-1}\left(\frac{1}{2} \sqrt{2}\right)$
Marking guidance:

Allow use of $\pi=3.14 \ldots$ .
Allow $\sin ^{-1} 3 t=30$ .

$\sin ^{-1} 3 t=\frac{1}{6} \pi$ and hence $t=\frac{1}{6}$
Or exact equivalent.
Can use degrees if consistent.

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CAIE A-Level Mathematics AS 1.5.3 Inverse Trig Notation Questions question 1