Answered: Find the remaining trigonometric ratios…

Name: Find the remaining trigonometric ratios of θ based on sin θ = −1/2 and
Uploaded: 2024-03-20T06:46:55.000Z
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Description: Find the remaining trigonometric ratios of θ based on sin θ = −1/2 and θ is not in QIII

Trigonometry (11th Edition)

11th Edition

ISBN:9780134217437

Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels

Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels

Chapter1: Trigonometric Functions

Section: Chapter Questions

Problem 1RE: 1. Give the measures of the complement and the supplement of an angle measuring 35°.

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Find the remaining trigonometric ratios of θ based on sin θ = −1/2 and θ is not in QIII

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Step 1

Sin is negative in 3rd and 4th quadrant. Given that θ is not in the third quadrant. That means θ is in the 4th quadrant.

There cos and sec are positive only.

$cosθ = \sqrt{1 - \sin^{2} θ} = \sqrt{1 - {(- \frac{1}{2})}^{2}} = \frac{\sqrt{3}}{2} tanθ = \frac{sinθ}{cosθ} = \frac{(- \frac{1}{2})}{(\frac{\sqrt{3}}{2})} = - \frac{1}{\sqrt{3}} = - \frac{\sqrt{3}}{3}$

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