6. Trigonometric Identities and More Equations

Use the given information to find each of the following.

sin x, given cos 2x = 2/3 , with π < x < 3π/2

Simplify each expression.

√[(1 + cos 76°)/2]

Perform each transformation. See Example 2.

Write sec x in terms of sin x.

Use the even-odd identities to evaluate the expression.

$\cos\left(-\theta\right)-\cos\theta$

Use the even-odd identities to evaluate the expression.

$-\cot\left(\theta\right)\cdot\sin\left(-\theta\right)$

Select the expression with the same value as the given expression.

$\sec\left(-\frac{4\pi}{5}\right)$

Select the expression with the same value as the given expression.

$\sin\left(-38\degree\right)$