Q. 12 If sin胃=14聽and 胃聽is in secon... [FREE SOLUTION]

91影视

Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 12: Q. 12 (page 840)

If $\sin 胃 = \frac{1}{4}$ and $胃$ is in second quadrant, find
(a) $\cos 胃$ (b) $\tan 胃$
(c) $\sin (2 胃)$ (d) $\cos (2 胃)$
(e) $\sin (\frac{1}{2} 胃)$

Short Answer

Expert verified

(a) $\cos 胃 = - \frac{\sqrt{15}}{4}$

(b) $\tan 胃 = - \frac{1}{\sqrt{15}}$

(d) $\cos (2 胃) = \frac{7}{8}$

(e) $\sin (\frac{1}{2} 胃) = \frac{\sqrt{4 + \sqrt{15}}}{2 \sqrt{2}}$

Step by step solution

Step 1. Given Information

Given $\sin 胃 = \frac{1}{4}$ and $\frac{蟺}{2} < 胃 < 蟺$ .

Part (a) Step 1. Finding cosθ

We know that

$\cos^{2} 胃 + \sin^{2} 胃 = 1 \cos^{2} 胃 + {(\frac{1}{4})}^{2} = 1 \cos^{2} 胃 = 1 - \frac{1}{16} = \frac{15}{16} \cos 胃 = 卤 \frac{\sqrt{15}}{4} \cos 胃 = - \frac{\sqrt{15}}{4}$

Part (b) Step 1. Finding tanθ

$\tan 胃 = \frac{1 / 4}{- \sqrt{15} / 4} \tan 胃 = \frac{1}{4} 脳 \frac{- 4}{\sqrt{15}} \tan 胃 = - \frac{1}{\sqrt{15}}$

Part (c) Step 1. Finding sin2θ

$\sin (2 胃) = 2 脳 \frac{1}{4} 脳 - \frac{\sqrt{15}}{4} \sin (2 胃) = - \frac{\sqrt{15}}{8}$

Part (d) Step 1. Finding cos2θ

$\cos 2 胃 = {(- \frac{\sqrt{15}}{4})}^{2} - {(\frac{1}{4})}^{2} \cos 2 胃 = \frac{15}{16} - \frac{1}{16} = \frac{14}{16} = \frac{7}{8}$

Part (e) Step 1. Finding sin12θ

$\sin (\frac{1}{2} 胃) = \sqrt{\frac{1 - (- \frac{\sqrt{15}}{4})}{2}} \sin (\frac{1}{2} 胃) = \sqrt{\frac{1 + \frac{\sqrt{15}}{4}}{2}} \sin (\frac{1}{2} 胃) = \sqrt{\frac{4 + \sqrt{15}}{8}} \sin (\frac{1}{2} 胃) = \frac{\sqrt{4 + \sqrt{15}}}{2 \sqrt{2}}$

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91影视

If $\sin 胃 = \frac{1}{4}$ and $胃$ is in second quadrant, find
(a) $\cos 胃$ (b) $\tan 胃$
(c) $\sin (2 胃)$ (d) $\cos (2 胃)$
(e) $\sin (\frac{1}{2} 胃)$

Short Answer

Step by step solution

Step 1. Given Information

Part (a) Step 1. Finding cosθ

Part (b) Step 1. Finding tanθ

Part (c) Step 1. Finding sin2θ

Part (d) Step 1. Finding cos2θ

Part (e) Step 1. Finding sin12θ

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91影视

If sin胃=14and 胃is in second quadrant, find(a) cos胃 (b) tan胃(c) sin2胃 (d) cos2胃(e)sin12胃

Short Answer

Step by step solution

Step 1. Given Information

Part (a) Step 1. Finding cosθ

Part (b) Step 1. Finding tanθ

Part (c) Step 1. Finding sin2θ

Part (d) Step 1. Finding cos2θ

Part (e) Step 1. Finding sin12θ

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Statistics

Logic and Functions

Mechanics Maths

Calculus

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

If $\sin 胃 = \frac{1}{4}$ and $胃$ is in second quadrant, find
(a) $\cos 胃$ (b) $\tan 胃$
(c) $\sin (2 胃)$ (d) $\cos (2 胃)$
(e) $\sin (\frac{1}{2} 胃)$