Q. 40 If cos胃=14and theta is ni fourt... [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. 40 (page 486)

If $\cos 胃 = \frac{1}{4}$ and theta is ni fourth quadrant
find the exact value of
role="math" localid="1647345756702" $a) \sin 胃 b) \sin (胃 - \frac{蟺}{6}) c) \cos (胃 + \frac{蟺}{3}) d) \tan (胃 - \frac{蟺}{4})$

Short Answer

Expert verified

The values are

$a) \sin 胃 = - \frac{\sqrt{15}}{4} b) \sin (胃 - \frac{蟺}{6}) = \frac{- 3 \sqrt{5} - 1}{8} c) \cos (胃 + \frac{蟺}{3}) = \frac{1 + 3 \sqrt{5}}{8} d) \tan (胃 - \frac{蟺}{4}) = \frac{- \sqrt{15} - 1}{1 - \sqrt{15}}$

Step by step solution

Given information

We are given $\cos 胃 = \frac{1}{4}$

Find sinθ

We have,

$\sin 胃 = \sqrt{1 - \cos^{2} 胃} \sin 胃 = \sqrt{1 - {(\frac{1}{4})}^{2}} \sin 胃 = - \frac{\sqrt{3}}{2} a s t h e t a i s i n f o u r t h q u a d r a n t$

Find sin(θ-π6)

We know that

$\sin (胃 - \frac{蟺}{6}) = \sin 胃 \cos \frac{蟺}{6} - \cos 胃 \sin \sin (胃 - \frac{蟺}{6}) = - \frac{\sqrt{15}}{4} (\frac{\sqrt{3}}{2}) - (\frac{1}{4}) (\frac{1}{2}) \sin (胃 - \frac{蟺}{6}) = - \frac{\sqrt{45}}{8} - \frac{1}{8} \sin (胃 - \frac{蟺}{6}) = \frac{- 1 - 3 \sqrt{5}}{8}$

Find cos(θ+π3)

We have,

$\cos (胃 + \frac{蟺}{3}) = \cos (胃) \cos (\frac{蟺}{3}) - \sin (胃) \sin (\frac{蟺}{3}) \cos (胃 + \frac{蟺}{3}) = \frac{1}{4} 路 \frac{1}{2} - (- \frac{\sqrt{15}}{4}) (\frac{\sqrt{3}}{2}) \cos (胃 + \frac{蟺}{3}) = \frac{1 + 3 \sqrt{5}}{8}$

Find tan(θ-π4)

We have,

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91影视

If $\cos 胃 = \frac{1}{4}$ and theta is ni fourth quadrant
find the exact value of
role="math" localid="1647345756702" $a) \sin 胃 b) \sin (胃 - \frac{蟺}{6}) c) \cos (胃 + \frac{蟺}{3}) d) \tan (胃 - \frac{蟺}{4})$

Short Answer

Step by step solution

Given information

Find sinθ

Find sin(θ-π6)

Find cos(θ+π3)

Find tan(θ-π4)

One App. One Place for Learning.

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91影视

If cos胃=14and theta is ni fourth quadrantfind the exact value ofrole="math" localid="1647345756702" a)sin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 sinθ

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

Statistics

Probability and Statistics

Discrete Mathematics

Logic and Functions

Geometry

Pure Maths

Study anywhere. Anytime. Across all devices.

If $\cos 胃 = \frac{1}{4}$ and theta is ni fourth quadrant
find the exact value of
role="math" localid="1647345756702" $a) \sin 胃 b) \sin (胃 - \frac{蟺}{6}) c) \cos (胃 + \frac{蟺}{3}) d) \tan (胃 - \frac{蟺}{4})$