Right Triangle Trig Practice Test

Pre-Calculus Right Triangle Trig PRACTICE Test 1. If sin 𝜃 = 1. sin 𝜃 = 2 9 2 9 2 1. sin 𝜃 = 9 , find the other five trig functions. cos 𝜃 = √77 9 tan 𝜃 = 2√77 77 9 csc 𝜃 = 2 sec 𝜃 = 9√77 77 2. Find the EXACT value of x in the triangle. 15 45° csc 𝜃 = cos 𝜃 = sec 𝜃 = tan 𝜃 = cot 𝜃 = cot 𝜃 = √77 2 2.__________________ 𝒙 𝜋 𝜋 3. Evaluate without a calculator (you MUST show work!): sin 3 + cos 6 3.__________________ 4. Find the EXACT value of x in the triangle. 4.__________________ 30° 15 30° 𝑥 5. A student is standing 52 feet away from a flagpole that is 35 ft tall. Find the angle of elevation to the top of the flagpole. Draw a picture! Round to the nearest tenth. 5.__________________ 6. From the top of a 150 ft lighthouse, a ship is observed in the ocean at an angle of depression of 28°. How far is the ship from the base of the lighthouse? Draw a picture! Round to the nearest tenth. 6.__________________ 7. While traveling across flat land, you notice a mountain directly in front of you. The angle of elevation to the peak is 32°. After you drive 12 miles closer to the mountain, the angle of elevation is 46°. Approximate the height of the mountain to the nearest tenth of a mile. Draw a picture! 7.__________________ 8. A ship leaves port at 9:00 a.m. and has a bearing of 𝑁 70° 𝑊. The ship sails at 18 knots. How many nautical miles north and how many nautical miles west will the ship have traveled by 1:00 p.m.? Draw a picture! Round to the nearest tenth. 8. north:____________ 9. A plane is 80 miles south and 35 miles east of an airport. The pilot wants to fly directly to the airport. What bearing should be taken? Draw a picture! 9.__________________ west:_____________ 10. Find the sign of (𝐬𝐢𝐧𝟐 𝜽)(𝐬𝐞𝐜 𝜽) if 𝜃 lies in QII. 10._________________ 11. Find the quadrant in which 𝜃 lies if tan 𝜃 > 0 and csc 𝜃 < 0. 11._________________ 3 12. Find the values of the other trig functions if cos 𝜃 = − 5 and 𝜃 lies in Quadrant II. 13. Find the exact value of cos 11𝜋 . 6 csc 𝜃 = 3 cos 𝜃 = − 5 sec 𝜃 = tan 𝜃 = cot 𝜃 = 13._________________ 14. Find the exact value of tan 270°. 15. Find the terminal point determined by t = 12. sin 𝜃 = 14._________________ 21𝜋 . 4 15._________________ Trig Practice Test Answers 2 1. sin 𝜃 = 9 2. cos 𝜃 = √77 9 tan 𝜃 = 2√77 77 csc 𝜃 = 2 9 sec 𝜃 = 9√77 77 cot 𝜃 = √77 2 tan 𝜃 = −4 3 csc 𝜃 = 4 5 sec 𝜃 = −5 3 cot 𝜃 = −3 4 15√2 2 3. √3 4. 10√3 5. 33.9° 6. 282.1 ft 7. 18.9 miles 8. North: 24.6 West: 67.7 9. 𝑁 23.6° 𝑊 10. Negative 11. Q3 4 12. sin 𝜃 = 5 13. √3 2 14. Undefined √2 15. ( 2 , − √2 ) 2 cos 𝜃 = −3 5