University:
North Central College
Course:
MATH 140 | Precalculus
Academic year:

2021
Views:

33

Pages:

2
Author:

Giovanni Pope

Honors Pre-Calculus Review #2 Quiz 4.1-4.4 All questions with a * would be calculator problems! 1a. Convert 25°15'25'' to a decimal. 25.257 1b. Convert 135.29° to a Degree/Minute/Second. 135°17'04'' 2a. Convert 15° to a radian in terms of π. 15° * (π/180) = π/12 2b. Convert 5π/7 to a degree. (round to the nearest 100th) (5π/7) * (180/π) = 128.57° 3. If the radius of a compact disk is 6 cm. Find the linear speed of a point on the circumference of the disc if it is rotating at a speed of 500 RPMs. 500 rev/min * 2π(6) cm/1 rev = 18,849.56 cm/min 4. Find the six Trig. Functions of the angle θ (No Decimal answers!) θ = -11π/6 sin(-11π/6) = 1/2 csc(-11π/6) = 2 cos(-11π/6) = √3/2 sec(-11π/6) = 2√3 tan(-11π/6) = √3/3 cot(-11π/6) = √3 5. The point (-2,10) is on the terminal side of an angle in standard position. Determine the exact values of the six trig functions. (Exact Please) sinθ = 10/√220 = 5/√26 = 5√26/26 cscθ = √26/5 cosθ = -2/√220 = -1/√26 = -√26/26 secθ = -√26 tanθ = 10/-2 = -5 cotθ = -1/5 6. Use a Calculator to determine(nearest 100th) a. cos(84°) = 0.105 b. csc(1.35) = 1.025 7. Use Trigonometric Identities to simplify: a. csc²(θ) - tan²(θ) csc²(θ) - tan²(θ) = 1/sin²(θ) - sin²(θ)/cos²(θ) = (cos²(θ) - sin²(θ)) / (sin²(θ)cos²(θ)) = cot²(θ) b. cot(θ)tan(θ) cot(θ)tan(θ) = (cos(θ)/sin(θ)) * (sin(θ)/cos(θ)) = 1 8. If secθ = 6/5 and tanθ < 0, find: cscθ = -√11/5 9. A passenger in an airplane flying at an altitude of 37,000 ft sees two towns directly to the west of the airplane. The angles of depression to the towns are 32 degrees and 76 degrees. How far apart are the towns? tan(32°) = 37000/y y ≈ 59212.38 tan(76°) = 37000/x x ≈ 9225.14 distance between towns = y - x ≈ 49987.24 ft Answers 1a. 25.256° 1b. 135°17'24" 2a. π/12 2b. 128.57° 3. 18,849.56 cm/min 4. sinθ = 1/2, cosθ = √3/2, tanθ = √3/3, cscθ = 2, secθ = 2√3, cotθ = √3 5. sinθ = 5/√26, cosθ = -√26/26, tanθ = -5, cscθ = √26/5, secθ = -√26, cotθ = -1/5 6a. 105 6b. 1.025 7a. cotθ 7b. sec²θ 8. -√11/5 9. 49,987 ft