# 7.7.1-eg - Example Evaluate the following √ 3 −1(i sin...

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Unformatted text preview: Example Evaluate the following: √ 3 −1 (i) sin − 2 (ii) tan−1 √ 3 (iii) sec−1(1) Solution: √ √ 3 3 − (i) The quantity sin , equivalently, arcsin − , is that angle θ ∈ [−π/2, π/2] 2 2 for which √ 3 sin θ = − . 2 √ But for θ = −π/3 it follows that sin θ = − 3/2, so √ 3 π −1 sin − =− . 2 3 −1 (ii) tan−1 √ 3 is that angle θ ∈ (−π/2, π/2) for which tan θ = But tan(π/3) = √ √ 3. 3 so it follows that tan−1 √ 3= π . 3 (iii) To evaluate sec−1 (1) = arcsec−1 (1), one must determine the angle θ ∈ [0, π/2) ∪ (π/2, π ] which uniquely satisﬁes sec(θ) = 1, or cos(θ) = 1 = 1. 1 Since cos(0) = 1, it follows that sec−1 (1) = 0. Note: For an easy way to remember the trigonometric functions at standard angles, see the document Notes on sine and cosine functions which is linked to the statement of the WeBWorK problem. ...
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## This note was uploaded on 04/02/2012 for the course MTH 132 taught by Professor Kihyunhyun during the Fall '10 term at Michigan State University.

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