6. Trigonometric Identities and More Equations

In a $\mathrm{circle}$, if two $\mathrm{chords}$ are $\mathrm{congruent}$, what can be said about the $\mathrm{arcs}$ they subtend?

Use the given information to find each of the following.

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

In the context of the $unit circle$, which of the following best represents an $intercepted arc$?

Which of the following correctly expresses the relationship between the length of an arc $s$ of a circle, its radius $r$, and the central angle $\theta$ in radians?

Which equation results from applying the secant and tangent segment theorem to the figure?

Which of the following is not a variation of a Pythagorean identity?

Which of the following is a correct Pythagorean trigonometric identity?

Simplify each expression.

√[(1 + cos 76°)/2]

Which of the following is not a variation of a Pythagorean identity?

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.

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