6. Trigonometric Identities and More Equations

In Exercises 47–54, use the figures to find the exact value of each trigonometric function. sin(θ/2)

In Exercises 47–54, use the figures to find the exact value of each trigonometric function. tan(θ/2)

In Exercises 59–68, verify each identity. $\cot \frac{x}{2}=\frac{\sin x}{1-\cos x}$

Be sure that you've familiarized yourself with the second set of formulas presented in this section by working C5–C8 in the Concept and Vocabulary Check. In Exercises 9–22, express each sum or difference as a product. If possible, find this product's exact value. sin 6x + sin 2x

Be sure that you've familiarized yourself with the second set of formulas presented in this section by working C5–C8 in the Concept and Vocabulary Check. In Exercises 9–22, express each sum or difference as a product. If possible, find this product's exact value. sin 7x ﹣ sin 3x

Be sure that you've familiarized yourself with the second set of formulas presented in this section by working C5–C8 in the Concept and Vocabulary Check. In Exercises 9–22, express each sum or difference as a product. If possible, find this product's exact value. cos 4x + cos 2x

Be sure that you've familiarized yourself with the second set of formulas presented in this section by working C5–C8 in the Concept and Vocabulary Check. In Exercises 9–22, express each sum or difference as a product. If possible, find this product's exact value. sin x + sin 2x

Be sure that you've familiarized yourself with the second set of formulas presented in this section by working C5–C8 in the Concept and Vocabulary Check. In Exercises 9–22, express each sum or difference as a product. If possible, find this product's exact value. cos 3x/2 + cos x/2

Be sure that you've familiarized yourself with the second set of formulas presented in this section by working C5–C8 in the Concept and Vocabulary Check. In Exercises 9–22, express each sum or difference as a product. If possible, find this product's exact value. sin 75° + sin 15°

Be sure that you've familiarized yourself with the second set of formulas presented in this section by working C5–C8 in the Concept and Vocabulary Check. In Exercises 9–22, express each sum or difference as a product. If possible, find this product's exact value. cos 75° ﹣ cos 15°

Find values of the sine and cosine functions for each angle measure.

B, given cos 2B = 1/8 , 540° < 2B < 720°

Find values of the sine and cosine functions for each angle measure.

2y, given sec y = -5/3, sin y > 0

Use the given information to find each of the following.

sin A/2, given cos A/2 = - 3, 90° < A < 180°

Use the given information to find each of the following.

sin y, given cos 2y = -1/3 , π/2 < y < π

Use the given information to find each of the following.

sin 2x, given sin x = 0.6, π/2 < y < π