Math Trigonometry Quiz 1 Review Key

Algebra 2 Honors Trig Quiz 1 Review The following problems should be done quickly and without a scientific calculator only. 1. Find the degree measure of an angle   in standard position determined by the rotation of the initial ray through one and two-thirds of a clockwise revolution.   1 2/3 * (-360) = -600° 2. Find the degree measure of an angle in standard position determined by the rotation of the initial ray through four-fifths of a counter-clockwise revolution. 4/5 * 360 = 288° Write a formula for the measures of all angles coterminal with the given angle. Then use the formula to find two angles, one positive and one negative, that are coterminal with the given angle.   3. θ = 370° 370 + 360n, where n is an integer 10° and -350° 4. θ = 5π/7 5π/7 + 2πn, where n is an integer 19π/7 and -9π/7 Express in either "Decimal Degrees" or in "Degrees Minutes Seconds" to the nearest second. 5. 73.03° 6. 119°21'0" 7. 16.24° 8. 74°53'24" Find a first-quadrant angle θ, for which an angle four times as large as θ will be in the given quadrant. 9. Quadrant 1 0° < 4θ < 90° 0° < θ < 22.5° 10. Quadrant 2 90° < 4θ < 180° 22.5° < θ < 45° 11. Quadrant 3 180° < 4θ < 270° 45° < θ < 67.5° 12. Quadrant 4 270° < 4θ < 360° 67.5° < θ < 90° 13. Consider an angle θ whose terminal side passes through (-12, -5). Find the value of the remaining five trig functions. sinθ = -5/13 cosθ = -12/13 tanθ = 5/12 cscθ = -13/5 secθ = -13/12 cotθ = 12/5 14. Find the six trig functions of θ. [Image of a right triangle with sides 3 and 4, hypotenuse 5] sinθ = 3/5 cosθ = 4/5 tanθ = 3/4 cscθ = 5/3 secθ = 5/4 cotθ = 4/3 15. If sinθ = 5/6 and cosθ < 0, find the other five trig functions. [Image of a right triangle with hypotenuse 6 and opposite side 5] cosθ = -√11/6 tanθ = -5√11/11 cscθ = 6/5 secθ = -6√11/11 cotθ = -√11/5 Find the exact value for x and y. 16. x/10 = √3/2 2x = 10√3 x = 5√3 18. x/9 = 1/√2 x√2 = 9 x = 9√2/2 19. 24/y = 1/√3 y = 24√3 x = 12√3 20. 32/y = √3/2 4y = 32√3 y = 8√3 x = 4√3 21. y/80 = √3/2 2y = 80√3 y = 40√3 x = 20√3 Determine the measurements for angle θ for each of the following triangles. Round to the nearest hundredth of a degree. 22. sinθ = 13/15 θ = 59.04° 23. cosθ = 5/11 θ = 63.94° 24. tanθ = 15/8 θ = 61.93° Draw a picture for each! Round all answers to the nearest thousandth. 25. An airplane is at an elevation of 35,000 ft when it begins its approach to an airport. Its angle of descent is 6°. What is the approximate air distance between the plane and the airport? 26. Find the measures of the acute angles of a right triangle whose legs are 9 cm and 16 cm long. [Image of a right triangle with legs 9 and 16] tanθ = 9/16 θ = 29.36° α = 60.64° 27. Find the measures of the angles of an isosceles triangle whose sides are 5, 10, and 10. [Image of an isosceles triangle with sides 5, 10, and 10] cosθ = 2.5/10 θ = 75.52° Angles: 75.52°, 75.52°, 28.96° 28. An engineer builds a 75-foot vertical cellular phone tower. Find the angle of elevation to the top of the tower from a point on level ground 95 feet from its base.   tanθ = 75/95 θ = 38.29° 29. 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 35° and 45° respectively. Find the tower's height.   tan(45°) = x/y tan(35°) = x/(y+12) y*tan(45°) = x y*tan(35°) + 12*tan(35°) = x tan(45°) = y*tan(35°) + 12*tan(35°) y = 8.40249 x = 28.0276 m 30. 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 75 ft from the flagpole. Find the height of the flagpole.   tan(27°) = x/75 x = 38.2144 Flagpole: 59.21 ft 31. While traveling across flat land, you notice a mountain directly in front of you. The angle of elevation to the peak is 6.5°. After you drive 16 miles closer to the mountain, the angle of elevation is 14°. Approximate the height of the mountain.   tan(6.5°) = x/(16+y) tan(14°) = x/y y*tan(14°) = x 16*tan(6.5°) + y*tan(6.5°) = x y = 13.464 x = 3.357 miles