Algebra and Trigonometry: Structure and Method, Book 2
Algebra and Trigonometry: Structure and Method, Book 2
2000th Edition
ISBN: 9780395977255
Author: MCDOUGAL LITTEL
Publisher: McDougal Littell
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Chapter 13.9, Problem 5ST

(a)

To determine

To find: The value of cos2θ.

(a)

Expert Solution
Check Mark

Answer to Problem 5ST

The cos2θ=41841 .

Explanation of Solution

Given information:

The given information is 180<θ<360 and cosθ=2129 .

Calculation:

We know that cos2θ=cos2θsin2θ .

Now, we have to find cos2θ and sin2θ .

  cos2θ=(2129)2cos2θ=(441841)

We know that sin2θ=1cos2θ .

  sin2θ=1cos2θsin2θ=1441841sin2θ=400841

Now,

  cos2θ=cos2θsin2θcos2θ=441841400841cos2θ=41841

Therefore, the cos2θ=41841 .

(b)

To determine

To find: The value of sin2θ.

(b)

Expert Solution
Check Mark

Answer to Problem 5ST

The sin2θ=840841 .

Explanation of Solution

Given information:

The given information is 180<θ<360 and cosθ=2129 .

Calculation:

We know that sin2θ=2sinθcosθ .

Now, we have to find sinθ .

We know that sin2θ=400841 .

  sin2θ=400841sinθ=400841sinθ=±2029

Since sinθ is negative in the third and fourth quadrant, we can take value as sinθ=2029

  sin2θ=2sinθcosθsin2θ=2(2029)(2129)sin2θ=840841

Therefore, the sin2θ=840841 .

(c)

To determine

To find: The value of cos(θ2).

(c)

Expert Solution
Check Mark

Answer to Problem 5ST

The cos(θ2)=22929 .

Explanation of Solution

Given information:

The given information is 180<θ<360 and cosθ=2129 .

Calculation:

We know that cos(θ2)=±1+cosθ2 .

Substitute the value of cosθ in the equation

  cos(θ2)=±1+cosθ2cos(θ2)=±1+(2129)2cos(θ2)=±2921292

  cos(θ2)=±8292cos(θ2)=±429cos(θ2)=±2129

Multiply the numerator and the denominator by 29 .

  cos(θ2)=±2129(2929)cos(θ2)=±22929

From the given interval for we find that 90°<θ2<180° Sine cosine function is negative in the third quadrant, we need take only the negative value for cos(θ2) .

Therefore, the cos(θ2)=22929 .

Chapter 13 Solutions

Algebra and Trigonometry: Structure and Method, Book 2

Ch. 13.1 - Prob. 11OECh. 13.1 - Prob. 12OECh. 13.1 - Prob. 13OECh. 13.1 - Prob. 1WECh. 13.1 - Prob. 2WECh. 13.1 - Prob. 3WECh. 13.1 - Prob. 4WECh. 13.1 - Prob. 5WECh. 13.1 - Prob. 6WECh. 13.1 - Prob. 7WECh. 13.1 - Prob. 8WECh. 13.1 - Prob. 9WECh. 13.1 - Prob. 10WECh. 13.1 - Prob. 11WECh. 13.1 - Prob. 12WECh. 13.1 - Prob. 13WECh. 13.1 - Prob. 14WECh. 13.1 - Prob. 15WECh. 13.1 - Prob. 16WECh. 13.1 - Prob. 17WECh. 13.1 - Prob. 18WECh. 13.1 - Prob. 19WECh. 13.1 - Prob. 20WECh. 13.1 - Prob. 21WECh. 13.1 - Prob. 22WECh. 13.1 - Prob. 23WECh. 13.1 - Prob. 24WECh. 13.1 - Prob. 25WECh. 13.1 - Prob. 26WECh. 13.1 - Prob. 27WECh. 13.1 - Prob. 28WECh. 13.1 - Prob. 29WECh. 13.1 - Prob. 30WECh. 13.1 - Prob. 31WECh. 13.1 - Prob. 32WECh. 13.1 - Prob. 33WECh. 13.1 - Prob. 34WECh. 13.1 - Prob. 35WECh. 13.1 - Prob. 36WECh. 13.1 - Prob. 37WECh. 13.1 - Prob. 38WECh. 13.1 - Prob. 39WECh. 13.1 - Prob. 40WECh. 13.1 - Prob. 41WECh. 13.1 - Prob. 42WECh. 13.1 - Prob. 43WECh. 13.1 - Prob. 44WECh. 13.1 - Prob. 45WECh. 13.1 - 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