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Given \cos \left ( \alpha \right )= -8/9 and \alpha is in quadrant II, find the exact value of...

Question:

Given {eq}\cos \left ( \alpha \right )=- 8/9 {/eq} and {eq}\alpha {/eq} is in quadrant II, find the exact value of {eq}\cos \left ( \alpha /2 \right ) {/eq}. Note: You are not allowed to use decimals in your answer.

{eq}\cos \left ( \alpha /2 \right ) {/eq} = .

Cosine's Double Angle Property:

The mathematical representation of the cosine double angle property in terms of the cosine function is:

  • {eq}\displaystyle \cos 2x=2\cos ^2x-1 {/eq}

Substitute the given value of cosine function in the formula and simplify the expression for the value of the second quadrant of the cosine function.

Answer and Explanation: 1

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The given value of cosine function is:

{eq}\displaystyle \cos \left ( \alpha \right )=-8/9 {/eq}

Using the formula of cosine double angle, we...

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Trigonometric Functions: Definition & Examples

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Chapter 3 / Lesson 6
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What are trigonometric functions? Learn more about all 6 trig functions, which formulas to use and examples of how to solve different trigonometric problems.


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