7.7.1-eg - Example Evaluate the following: √ 3 −1 (i)...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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. ...
View Full Document

Ask a homework question - tutors are online