## Related questions with answers

Question

Write the letter of the correct answer. If

$\sin \theta = \frac { 2 } { 3 }$

, then

$\cos 2 \theta =$

__.

Solution

VerifiedAnswered 2 years ago

Answered 2 years ago

Step 1

1 of 3Given in problem : $\sin\theta=\dfrac{2}{3}$

To find the value of $\cos 2\theta$ we will use formula $\cos2\theta=\cos^2\theta-\sin^2\theta$ so we need first find the value of $\cos^2 theta$. So we have :

$\begin{align*} \cos^2 \theta&=1-\sin^2\theta &&\text{\color{#4257b2}Pythagorean identity $\sin^2x+\cos^2x=1$}\\ \\ &=1-\left(\dfrac{2}{3}\right)^2&&\text{\color{#4257b2}Putting the value}\\ \\ &=\dfrac{9-4}{9} &&\text{\color{#4257b2}Taking LCM}\\ \\ &=\dfrac{5}{9} &&\text{\color{#4257b2}Simplifying} \end{align*}$

## Create an account to view solutions

By signing up, you accept Quizlet's Terms of Service and Privacy Policy

## Create an account to view solutions

By signing up, you accept Quizlet's Terms of Service and Privacy Policy

## Recommended textbook solutions

#### Algebra 2 Common Core

1st Edition•ISBN: 9780133186024 (2 more)Basia Hall, Charles, Kennedy7,537 solutions

#### Algebra and Trigonometry: Structure and Method, Book 2

1st Edition•ISBN: 9780395977255 (1 more)Brown, Dolciani, Kane, Sorgenfrey8,447 solutions

#### Big Ideas Math Algebra 2: A Common Core Curriculum

1st Edition•ISBN: 9781608408405Boswell, Larson5,067 solutions

## More related questions

- prealgebra

1/4

- prealgebra

1/7