NOTES Show all necessary work. You are not allowed to use your unit circle on the test. The test will include a non-calculator portion

Transcription

1 Algebra Trig hapter 1 Review Problems omplete the following problems on a separate piece of paper. NOTES Show all necessary work. You are not allowed to use your unit circle on the test. The test will include a non-calculator portion 1-1 Right Triangle Trig 1. Use the triangle at right to find each of the six trigonometric functions of θ Use simplified radical form.. Find the value of x. a) b) x 100mm A θ I need to use: soh cah toa x 1. When a 6-foot tall pole casts a 4-foot shadow, what is the angle of elevation of the sun? (Round the nearest degree). 1. Angles and Angle Measure 5. Draw each angle in standard position: a. 5 b. 190 c I can add or subtract Find positive angles coterminal with each of the following: a. 400 b c. 0

2 1-4 Law of Sines 7. Find the area of each triangle: a. A b. =, a = 18, b = Solve DA. (You may get 0, 1 or solutions!!) a. A= 50, a = 4, b = 40 b. A= 4, a =, b = 8 c. A= 15, a =, b = Sarah Phillips, an officer for the Department of Fisheries and Wildlife, checks boaters on a lake to make sure they do not disturb two osprey nesting sites. She leaves a dock and heads due north in her boat to the first nesting site. From here, she turns 5 north of due west and travels an additional.14 miles to the second nesting site. She the travels 6.7 miles directly back to the dock. How far from the dock is the first nesting site? Round to the nearest tenth. 1-5 Law of osines 10. Solve DA. a. = 5, a = 5, b = 8 b. = 71, c = 6, a = 11 c. a = 16.4, b= 1.1, c = A balloonist is directly above a straight road 1.5 miles long that joins two villages. she find that the town closer to her is at an angle of depression of 5 and the farther town is at an angle of depression of 1. How high above the ground is the balloon?

3 1./1.6 Trigonometric Functions of General Angles 1. Find the reference angle for each of the following a. b. -10 c Find the exact value of each expression. Do not use a calculator or unit circle. 1π 7π a. tan 10 b. cot (-10 ) c. csc 510 d. cos e. sec f. sin 4 6 9π cos60 + sin 0 g. cos h. csc8π i. j. (sin 0 ) + (cos0 ) Inverse Trigonometric Functions 14. Find the exact value of each expression. Do not use a calculator. a. Sin -1 1 b. os -1 1 c. Tan -1 d. arccos e. tan(sin -1 1 )

4 h 1 Review Answers LANK WORKSHEET -PAGE DOWN omplete the following problems on a separate piece of paper. NOTES Show all necessary work. You are not allowed to use your unit circle on the test. The test will include a non-calculator portion 1-1 Right Triangle Trig 1. Use the triangle at right to find each of the six trigonometric functions of θ Use simplified radical form sinθ = cosθ = tan θ θ = cscθ = secθ = cotθ = Find the value of x. a) b) x x tan = A tan x = x = 4. 5mm 100mm 1 x = I need to use: soh cah toa x. When a 6-foot tall pole casts a 4-foot shadow, what is the angle of elevation of the sun? (Round the nearest degree). 6 tan x = Angles and Angle Measure 4 x = Draw each angle in standard position: a. 5 b. 190 c I can add or subtract Find positive angles coterminal with each of the following: a. 400 b c

5 1-4 Law of Sines 7. Find the area of each triangle: a. A b. =, a = 18, b = 15 Area= 6.9un Area =71.55un 8. Solve DA. (You may get 0, 1 or solutions!!) a. A= 50, a = 4, b = 40 = 64, = 66, c = # = 116, = 14, c = b. A= 4, a =, b = 8 c. A= 15, a =, b = 15 = 4, = 1, c = Sarah Phillips, an officer for the Department of Fisheries and Wildlife, checks boaters on a lake to make sure they do not disturb two osprey nesting sites. She leaves a dock and heads due north in her boat to the first nesting site. From here, she turns 5 north of due west and travels an additional.14 miles to the second nesting site. She the travels 6.7 miles directly back to the dock. How far from the dock is the first nesting site? Round to the nearest tenth miles 1-5 Law of osines 10. Solve DA. a. = 5, a = 5, b = 8 b. = 71, c = 6, a = 11 c. a = 16.4, b= 1.1, c = 18.5 A = 6, = 109 c = =, A = 77, b = = 58, A = 48, = A balloonist is directly above a straight road 1.5 miles long that is between villages. She notes that the angle of depression to the village closest to her is 5 and the angle of depression to the other village is 1. How high above the ground is the balloon?.485miles

6 1./1.6 Trigonometric Functions of General Angles 1. Find the reference angle for each of the following a. b. -10 c. 15 π Find the exact value of each expression. Do not use a calculator or unit circle. 1π 7π a. tan 10 b. cot (-10 ) c. csc 510 d. cos e. sec f. sin 4 6 9π g. cos h. csc8π i. cos60 + sin undefined 1 4 j. (sin 0 ) + (cos0 ) 1.7 Inverse Trigonometric Functions 14. Find the exact value of each expression. Do not use a calculator. a. Sin -1 1 b. os -1 1 c. Tan -1 d. arccos e. tan(sin -1 1 )

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