inverse trig question (1 Viewer)

Abhiram Yanamandra · Jun 30, 2019

Please help me with this question.
find the exact value of sin(cos^-1(2/3)+tan^-1(-3/4))
the image of this question is down below, if that help seeing the question better.

Drongoski · Jun 30, 2019

To better understand: draw 2 associated right-angled triangles:
1) angle theta, with sides 2, root 5, 3
2) angle phi, with sides 3,4,5

$cos \theta = \frac{2}{3} $ $ sin \theta = \frac {\sqrt 5}{3} \\ \\ tan \phi = \frac {3}{4} $ $ sin \phi = \frac {3}{5} $ $ cos \phi = \frac {4}{5} \\ \\ \therefore $expression $ = sin(\theta - \phi) = sin \theta cos \phi - cos \theta sin \phi \\ \\ = \frac {\sqrt 5} {3} \times \frac {4}{5} - \frac {2}{3} \times \frac {3}{5} = \frac {4 \sqrt 5 - 6}{15} $$

inverse trig question (1 Viewer)

Abhiram Yanamandra

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Drongoski

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