Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Trigonometry Name ________________________________ Unit 1 Test Review Date ______________________ Read each question carefully. Show your work for full credit. Leave all answers in exact form, unless otherwise indicated. 1. Which quadrant has positive x-values and negative y-values? ___________________ 2. What is the radius of the Unit Circle? ___________________ 3. What is the circumference of the Unit Circle? ___________________ 4. Sketch the angle 2 . Then find sin( ), cos( ), and tan( ) for the angle. 3 sin( ) = _____________ cos( ) = ______________ tan( ) = _____________ 5. Sketch the angle 11 . Then find sin( ), cos( ), and tan( ) for the angle. 6 sin( ) = _____________ cos( ) = ______________ tan( ) = _____________ Convert from degrees to radians or radians to degrees. Show your work. 6. -125° = ______________ 7. 4 = ________________ 45 Coterminal Angles 8. Find two coterminal angles (one positive and one negative) of . _________ , _________ 3 Evaluate each of the following: 9. 12. 15. sin = ______ 4 10. 5 tan = ______ 6 11. 7 sin = ______ 2 13. sec = ______ 3 14. 5 cot = ______ 4 2 csc = ______ 3 16. sec2 = ______ 17. 9 cos = ______ 2 18. 4cos603tan = ______________ 4 20. The point (3,5) is on the terminal side of an angle in standard position. Find the exact value of all six trigonometric function values for the angle . 19. sin = ___________ cos = ___________ tan = ___________ csc = ___________ sec = ___________ cot = ___________ cos = ______ 3 tan sin 3 = ___________ 2 Arc Length, Area of a Sector, Angular Speed and Linear Speed 21. Find the length of an arc on a circle with a radius of 5 meters intercepted by a central angle 4 of radians. 3 22. Find the area of the sector of a circle with a central angle of 3.4 radians and a radius of 5.2 inches. 23. A sprinkler can water a lawn up to a distance of 50 feet. It turns through an angle of 120°. Find the area of the lawn that can be watered by this sprinkler. 24. A wheel has a diameter of 100 cm. If the wheel is supporting a craft moving at 45 kilometers per hour, then what is the angular velocity of the wheel, to the nearest whole number of revolutions per minute. 25. A bicycle wheel has a diameter of 78 cm. If the wheel revolves at a rate of 120 revolutions per minute, what is the linear velocity of the bike, in kilometers per hour? Round your answer to the nearest tenth. 26. Assume that the Earth’s orbit is circular, with a radius of 93,000,000 miles, and let “one year” equal 365.25 days. Under these conditions, find the linear velocity of the Earth in miles per second. Round to the nearest whole number of miles. 27. A train is travelling at the rate of 10 mph on a curve of radius 2000 feet. Through what angle will the train turn in one minute? Round to the nearest whole number of degrees.