`sin(arccos(-2/3))` Find the exact value of the expression. (Hint: Sketch a right triangle.)

Textbook Question

Chapter 4, 4.7 - Problem 61 - Precalculus (3rd Edition, Ron Larson).
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loves2learn | (Level 3) Salutatorian

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We know that

`cos(arccos(-2/3)) = -2/3`

Therefore, using trig identities,

=> `sin = sqrt(1 - cos^2) = sqrt(1 - 4/9)`

Thus,
=> `sin = sqrt(5/9) = sqrt(5)/3`

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