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

2019
Views:

193

Pages:

5
Author:

McGowanfgu

HPC Midterm Review Chapter 4: Trigonometric Functions 1. Find, if possible, the complement and supplement of the angle. a. 104° Complement: none Supplement: 76° b. 10π/9 Complement: none Supplement: 7π/9 2. A circle has a radius of 7 inches. Find the length of the arc intercepted by a central angle of 240°. S = r * θ = 7 * 240° * (π/180°) = 29.3 inches 3. The circular blade on a saw has a radius of 4 inches and rotates at 2400 revolutions per minute. a. Find the angular speed in radians per second. 2400 rev/min * (2π rad/rev) * (1 min/60 sec) = 251.3 rad/sec b. Find the linear speed of a blade tip in inches per second. 251.3 rad/sec * 4 inches = 1005.2 in/sec 4. A satellite in a circular orbit 1125 km above a planet makes one complete revolution every 120 minutes. Assuming that the planet is a sphere of radius 6400 km, find the linear speed of the satellite in kilometers per minute. Round your answer to the nearest whole number. r = 7525 km (2π * 7525 km) / 120 min ≈ 394 km/min 5. A truck is moving at a rate of 90 km per hour and the diameter of its wheels is 1.25 meters. Find the angular speed of the wheels in radians per minute. 90 km/hr * (1 hr/60 min) * (1000 m/1 km) * (2π rad/2(0.625)π m) = 2400 rad/min 6. Evaluate the six trigonometric functions if θ = -2π/3 sin(-2π/3) = -√3/2 cos(-2π/3) = -1/2 tan(-2π/3) = √3 csc(-2π/3) = -2/√3 sec(-2π/3) = -2 cot(-2π/3) = √3/3 7. Evaluate the trigonometric function. a. sin(-3π/4) = -√2/2 b. csc(2π/3) = 2/√3 c. tan(5π/3) = -√3 d. sec(-4π) = 1 e. cot(5π/2) = 0 f. cos(13π/6) = √3/2 8. Use the value of the trigonometric function to evaluate the indicated functions: sin(t) = 3/5 csc(-t) = -5/3 9. Find the values (in simplified form) of the six trigonometric functions of the angle shown in the figure. sinθ = 4/2√13 = 2/√13 = 2√13/13 cscθ = √13/2 cosθ = 6/2√13 = 3/√13 = 3√13/13 secθ = √13/3 tanθ = 2/3 cotθ = 3/2 10. Find the values (in simplified form) of the six trigonometric functions of the angle shown in the figure. sinθ = 1/5 cscθ = 5 cosθ = 2√6/5 secθ = 5/2√6 = 5√6/12 tanθ = 1/2√6 = √6/12 cotθ = 2√6 11. Simplify each expression. a. sinθ cosθ / (1 - cos²θ) sinθ cosθ / sin²θ = cosθ/sinθ = cotθ b. (sinθ + cosθ)² + (sinθ - cosθ)² sin²θ + 2sinθcosθ + cos²θ + sin²θ - 2sinθcosθ + cos²θ 2sin²θ + 2cos²θ = 2(sin²θ + cos²θ) = 2 c. tan²θ / (secθ + 1) + 1 (sec²θ - 1) / (secθ + 1) + 1 = (secθ + 1)(secθ - 1) / (secθ + 1) + 1 = secθ - 1 + 1 = secθ d. secθ - sinθ tanθ 1/cosθ - sinθ * sinθ/cosθ = 1/cosθ - sin²θ/cosθ = (1 - sin²θ) / cosθ = cos²θ/cosθ = cosθ e. cscθ tanθ 1/sinθ * sinθ/cosθ = 1/cosθ = secθ f. sinθ/cosθ + cosθ/sinθ (sin²θ + cos²θ)/(cosθsinθ) = 1/(cosθsinθ) = secθcscθ 12. John stands 150 meters from a water tower and sights the top at an angle of elevation of 36°. How tall is the tower? tan 36° = h/150 h ≈ 109 m 13. The Aerial Run in Snowbird, Utah has an angle of elevation of 20.2°. Its vertical drop is 2900 feet. Estimate the length of the run. sin 20.2° = 2900/x x ≈ 8398.57 ft