Use the Sum and Difference [Addition and Subtraction] Formulas to determine the exact value of each of the following.

cos (25/12 ) c. sin (5/12) d. tan ( 11/12 )

Use the Sum and Difference [Addition and Subtraction] Formulas to determine the exact value of each of the following.

sin (35/36 ) cos (13/18 ) cos (35/36 ) sin (13/18 ) c. tan(13/20 )+tan( /10)/ 1tan(13/20 ) tan( /10) d. cos (19/15 ) cos (4/15) + sin (19/15 ) sin (4/15) e. sin (5/7 ) cos (13/21 ) + cos (5/7 ) sin (13/21 ) f. tan(14/15 )tan( /10)/1+tan(14/15 ) tan( /10)

3. Find the exact value of the expressions sin( ) and cos( ) given that sin = 3 8, in quadrant II and cos = 12/13, in quadrant IV.

Find the exact value of each.

tan (cos1 1/5 sin1 3/5) c. cos (tan1 8/15 sin1 2/3)

Using the Sum and Difference Formulas, verify each identity. a. cos ( + /4) cos ( /4) = 2 sin b. sin 2 = 2 sin cos [Hint: use the fact that sin 2 = sin( + ).] c. cos 2 = cos2 sin2 d. tan 2 = 2 tan /1tan2

Use the Double Angle or Half Angle Formulas to determine the exact value of each of the following. a. 2 tan 15/1tan2 15 b. cos2 /8 sin2 /8 c. sin ( /12) cos ( /12) d. tan ( /12) e. sin(15)

Use the Half Angle Formulas to determine the exact value of cos (7/12). 3. Use the Sum and Difference Formulas to determine the exact value of cos (7/12). 4. Find the following values given sin = 4 7 and tan > 0. The quadrant in which terminates: _____ The quadrant in which 2 terminates: _____ sin 2 = _____ cos 2 = _____ tan 2 = _____

Find the following values given cos = 12/13 and tan < 0. The quadrant in which terminates: _____ The quadrant in which /2 terminates: _____ sin /2 = _____ cos /2 = _____ tan /2 = _____ 6. Find the following values given cos = 3/5 and tan > 0. The quadrant in which terminates: _____ The quadrant in which 2 terminates: _____ The quadrant in which /2 terminates: _____ tan 2 = _____ tan /2 = _____

Use the Power-Reducing Formulas to rewrite each expression as a single trig function raised to the first power. Box your final answer. a. sin4 3 b. (tan2 )(cos4 ) 8. Verify each identity. a. sin 2/sin = 2 cos b. cos 2/cos = 2 cos sec

Solve each equation. State all solutions in the interval [0, 2). a. 2 sin = 3 b. 3 tan + 3 = 0 c. 4 cot 4 = 0 d. 2 cos2 sin (/2 ) = 1 [HINT: use an identity or formula first]

sin 2 = cos [HINT: use an identity or formula first] f. sin = cos + 1 [HINT: square both sides - be sure to check your solutions] 2. Solve each equation. State ALL solutions. a. tan 3 = 0

3 csc() 2 = 0 c. tan sin2 = 3 tan d. 2 cos2 cos = 3

Solve each equation. State ALL solutions. a. 4 cot(5) + 4 = 0 b. cos cot2 = 3 cos c. 5 sin (/3 /2) = 0 Solve each equation. State all solutions in the interval [0, 2). a. 2 cos (/2) = 3 b. 2 sin2(4) = sin(4) + 1 c. 4 sin2(2) 1 = 0

Solve each equation. Use inverse trig functions to state your answer when necessary. (i) State ALL solutions. (ii) State all solutions in the interval [0, 2). a. 3 cos2 cos 2 = 0 b. csc2 2 cot = 4 [HINT: use an identity or formula and then factor] Solve the triangle. Give an EXACT answer for each unknown value [you may need to use a half- angle formula]. Simplify as much as possible. Box/circle your answers. = 60, = 45, and = 11.

Solve each triangle. Round your final answers to the nearest tenth. Box/circle your answers. a. = 109, = 42, and = 54. b. = 34.7, = 68.1, and = 43.9. c. = 33, = 25, and = 38.

d. = 6, = 12, and = 38. e. = 48.8, = 39.9, and = 22.

Two planets are orbiting a star. Planet B could be located at either of two possible positions, as shown in the figure below. Planet A is 50 million miles from the star, and Planet B is 35 million miles from the star. From Planet A, the viewing angle between the star and Planet B is 13. Find the possible distances form Planet A to Planet B. Round your answers to the nearest tenth of a million.

Solve each triangle. Round your final answers to the nearest tenth. Box/circle your answers. a. = 32.8, = 24.9, and = 12.4

b. = 4.4, = 6.2, and = 11.1 c. = 108, = 89.2, and = 23.1 2. Solve the for angle A given the side lengths of the triangle. Give an EXACT answer. Simplify as much as possible. Box/circle your answer. = 10, = 7, and = 8

Two airplanes leave an airport at the same time. An hour later, the planes are 204 km apart. If one plane has traveled 286 km and the other has traveled 198 km during the hour, find the angle between their flight paths. Round your final answer to the nearest tenth of a degree.

4. A triangle has three sides that measure 5, 6, and 10. Determine the measure of the largest angle. Give an exact answer in simplified form.

The beam of a searchlight situated at point C, from the deck of a Coast Guard search and rescue boat sweeps back and forth between two points, A and B, on shore. Point C is located 5 kilometers from point A and 8 kilometers from point B. The distance between A and B is 7 kilometers. a. Label the diagram below with the information provided. b. What is the angle, , through which the searchlight sweeps? Simplify completely.