Q. 39 if sin胃=13, is in quadrant 2 fi... [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 7: Q. 39 (page 486)

if $\sin 胃 = \frac{1}{3}$ , is in quadrant 2 find exact value of
$a) \cos 胃 b) \sin (胃 + \frac{蟺}{6}) c) \cos (胃 - \frac{蟺}{3}) d) \tan (胃 + \frac{蟺}{4})$

Short Answer

Expert verified

The values are

$a) \cos 胃 = - \frac{2 \sqrt{2}}{3} b) \sin (胃 + \frac{蟺}{6}) = \frac{\sqrt{3} - 2 \sqrt{2}}{6} c) \cos (胃 - \frac{蟺}{3}) = \frac{\sqrt{3} - 2 \sqrt{2}}{6} d) \tan (胃 + \frac{蟺}{4}) = \frac{- 1 + 2 \sqrt{2}}{2 \sqrt{2} + 1}$

Step by step solution

Given information

We are given $\sin 胃 = \frac{1}{3}$

Find cosθ

We have,

$\cos 胃 = \sqrt{1 - \sin^{2} 胃} \cos 胃 = \sqrt{1 - \frac{1}{9}} \cos 胃 = - \frac{2 \sqrt{2}}{3} a s 胃 i s i n 2 n d q u a d r a n t$

Find sin(θ+π6)

We have,

$\sin (胃 + \frac{蟺}{6}) = \sin 胃 \cos \frac{蟺}{6} + \sin \frac{蟺}{6} \cos 胃 \sin (胃 + \frac{蟺}{6}) = \frac{1}{3} (\frac{\sqrt{3}}{2}) + (- \frac{2 \sqrt{2}}{3}) (\frac{1}{2}) \sin (胃 + \frac{蟺}{6}) = \frac{\sqrt{3} - 2 \sqrt{2}}{6}$

Find cos(θ+π3)

We have,

$\cos (胃 - \frac{蟺}{3}) = \cos (胃) \cos (\frac{蟺}{3}) + \sin (胃) \sin (\frac{蟺}{3}) \cos (胃 - \frac{蟺}{3}) = (- \frac{2 \sqrt{2}}{3}) \frac{1}{2} + \frac{1}{3} (\frac{\sqrt{3}}{2}) \cos (胃 - \frac{蟺}{3}) = \frac{\sqrt{3} - 2 \sqrt{2}}{6}$

Find tan(θ+π4)

We have,

$\tan (胃 + \frac{蟺}{4}) = \frac{\tan (胃) + \tan (\frac{蟺}{4})}{1 - \tan (胃) \tan (\frac{蟺}{4})} \tan (胃 + \frac{蟺}{4}) = \frac{- \frac{1}{2 \sqrt{2}} + 1}{1 - (- \frac{1}{2 \sqrt{2}})} \tan (胃 + \frac{蟺}{4}) = \frac{- 1 + 2 \sqrt{2}}{2 \sqrt{2} + 1}$

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91影视

if $\sin 胃 = \frac{1}{3}$ , is in quadrant 2 find exact value of
$a) \cos 胃 b) \sin (胃 + \frac{蟺}{6}) c) \cos (胃 - \frac{蟺}{3}) d) \tan (胃 + \frac{蟺}{4})$

Short Answer

Step by step solution

Given information

Find cosθ

Find sin(θ+π6)

Find cos(θ+π3)

Find tan(θ+π4)

One App. One Place for Learning.

Most popular questions from this chapter

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91影视

if sin胃=13, is in quadrant 2 find exact value ofa)cos胃b)sin(胃+蟺6)c)cos(胃-蟺3)d)tan(胃+蟺4)

Short Answer

Step by step solution

Given information

Find cosθ

Find sin(θ+π6)

Find cos(θ+π3)

Find tan(θ+π4)

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Geometry

Statistics

Theoretical and Mathematical Physics

Pure Maths

Applied Mathematics

Study anywhere. Anytime. Across all devices.

if $\sin 胃 = \frac{1}{3}$ , is in quadrant 2 find exact value of
$a) \cos 胃 b) \sin (胃 + \frac{蟺}{6}) c) \cos (胃 - \frac{蟺}{3}) d) \tan (胃 + \frac{蟺}{4})$