Pre-Calculus Right Triangle Trigonometry Review Name Dec 201 Convert from Radians to Degrees, or Degrees to Radians 7π 1. 0 2.. 1. 11π. Find the si trig functions of θ. If sin θ =, find the other five trig functions. 7 Find the eact value for. 7. 8.. 0 10 1 0 Evaluate without using a calculator. 10. (sin ) 2 + (cos ) 2 11. (tan 0 ) 2 + (csc ) 2 12. sin π + cos π 1
Solve the triangle. Find all missing sides and angles, as eact values. 1. 1. y 0 y 8 Find the value of and/or y. Find an eact answer for in #1 and #17 1. 1. 2 2 y 8 17. 80 Determine the measurements for angle θ for each of the following triangles. Round to the nearest tenth of a degree. 18. 1. 20. θ 1 12 θ 11 1 θ 8 2
Applications: Draw a picture for each! Round all answers to the nearest tenth. 21. An airplane is at an elevation of,000 ft when it begins its approach to an airport. Its angle of descent is. a. What is the distance between the airport and the point on the ground directly below the airplane? b. What is the approimate air distance between the plane and the airport? 22. Find the measures of the acute angles of a right triangle whose legs are cm and 1 cm long. 2. Find the measures of the angles of an isosceles triangle whose sides are, 10, and 10. 2. An engineer builds a 7-foot vertical cellular phone tower. Find the angle of elevation to the top of the tower from a point on level ground feet from its base. 2. A skateboard ramp touches the ground at one point, and is ft off the ground at its highest point. The angle of elevation the ramp makes with the ground is 18.. What is the length of the ramp? 2. An escalator 12 feet in length rises to a platform and makes 0 angle with the ground. Find the height of the platform above the ground. 27. Points A and B (on the same side of a tower) are 12 m apart. The angles of elevation of the top of a tower are and respectively. Find the tower s height.
Applications: Draw a picture for each! Round all answers to the nearest tenth. 28. A student looks out of a second-story school window and sees the top of the school flagpole at an angle of elevation of 27. The student is 21 ft above the ground and 7 ft from the flagpole. Find the height of the flagpole. 2. While traveling across flat land, you notice a mountain directly in front of you. The angle of elevation to the peak is.. After you drive 1 miles closer to the mountain, the angle of elevation is 1. Approimate the height of the mountain. 0. A ship leaves port at 1 p.m. and has a bearing of S 18 E. The ship sails at 2 knots. How many nautical miles south and how many nautical miles east will the ship have traveled by :0 p.m.? 1. An airplane flying at 0 miles per hour has a bearing of. After flying for 2. hours, how far north and how far east has the plane traveled form its point of departure. 2. A plane is 10 miles north and 8 miles east of an airport. The pilot wants to fly directly to the airport. What bearing should be taken?. A ship is 80 miles east and 0 miles south of port. The captain wants to sail directly to port. What bearing should be taken?
Find the sign of the epression if the terminal point determined by θ is in the given quadrant.. cos θ tan θ; QIII. cos θ sec θ; Any Quadrant. tan θ sin θ cot θ ; QII 7. tan 2 θ sec θ; QII From the information given, find the quadrant in which θ lies. 8. sec θ > 0 and cot < 0. cot θ > 0 and cos > 0 0. tan θ > 0 and csc < 0 1. sin θ > 0 and cot < 0 Find the values of the other trig functions using the given information. 2. sin θ = 1 ; in Quadrant II. tan θ = 7 8 in Quadrant IV. cot θ = 0 in Quadrant I. csc θ = in Quadrant III Find the reference angle.. 0 7. 80 8. 2π. 1π
Find the eact value of the function WITHOUT a calculator. 0. sin 0 1. cot π 2. cos 1. tan π. sec 00. sin π. tan 7π 2 7. csc 1π 8. cos π Are the following points on the unit circle? Show your work.. ( 21, 20 10 ) 0. ( 2 2, 10 ) 10 10 The point P is on the unit circle. Find P(, y) from the given information. 1. The y-coordinate is 8 and P lies to the left of the y-ais 2. The -coordinate is and P is in Q Use the reference angles to find the terminal point determined by angle θ.. θ = 2π. θ = π. θ = 22
Answers 1. 2π 2. 210. 2π.. sin θ = cos θ = 7 tan θ = 7 7 csc θ = sec θ = 7 7 cot θ = 7. sin θ = cos θ = 11 tan θ = 11 11 csc θ = sec θ = 11 11 cot θ = 11 7. = 8. = 2 2. = 28 10. 1 11. 12. 2 1. =, y = 8 1. = 8, y = 7 1. = 1 1. =.72, y =. 17. = 20 18. θ = 7. 1. θ =. 20. θ = 1. 21. a.,002.8 ft 21b.,87.0 ft 22. 0. and 2. 2. 7. and 7. and 2 2. θ = 8. 2. l = 12.7 ft 2. h = 7 ft 27. h = 28.0 ft 28. h =.2 ft 2. h =.7 mi 0. S = 7. nm, E = 2.0 nm 1. N = 88.7 nm, E = 1018. nm 2. S 17.7 W or a bearing of 17.7 from the North. S 8 W or a bearing of 02 from the North. Negative. Positive. Positive 7. Negative 8. Q. Q1 0. Q 1. Q2 7
2. sin θ = 1 cos θ = 12 1 tan θ = 12 csc θ = 1 sec θ = 1 12 cot θ = 12. sin θ = 7 11 11 cos θ = 8 11 11 tan θ = 7 8 csc θ = 11 7 sec θ = 11 8 cot θ = 8 7. sin θ = 1 cos θ = 0 1 tan θ = 0 csc θ = 1 sec θ = 1 0 cot θ = 0. sin θ = 1 cos θ = 1 tan θ = 1 1 csc θ = sec θ = 1 1 cot θ = 1. θ = 7. θ = 0 8. θ = π. θ = π 0. 1 2 1. Undefined 2. 2 2.. 2. 2 2. Undefined 7. 2 8. 1 2. Yes 0. Yes 1. = 17 2. y = 7. ( 1, 2 ). ( 2 2, 2 2 2 ). ( 2 2, 2 2 ) 8