# 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

Become a Study.com member to unlock this answer! Create your account

View this answerThe given value of cosine function is:

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

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

See full answer below.

#### Ask a question

Our experts can answer your tough homework and study questions.

Ask a question Ask a question#### Search Answers

#### Learn more about this topic:

from

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