CAIE A-Level Mathematics AS 1.5.3 Inverse Trig Notation Questions

Practise applying sequences and series methods within the AS mathematics syllabus.

Exam points

use vector notation and operations
solve geometric problems with vectors
interpret vector relationships

[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