University:
Felician University
Course:
MATH-231 | Geometry I
Academic year:

2022
Views:

431

Pages:

4
Author:

Clint W.

EVALUATING INVERSE TRIG FUNCTIONS Find the EXACT Values using Inverse Trig Functions Domain/Range: arccos(√3/2) = 30°/π/6 arctan(-1) = -45°/-π/4 sin^(-1)(-1/2) = -30°/-π/6 cos^(-1)(0) = 90°/π/2 arcsin(sin(π/3)) = π/3 tan(arctan(√3/2)) = √3/2 tan(arccos(3/5)) = 4/3 (sin(tan^(-1)x))/(√(x^2+1)) = x/(√(x^2+1)) Use a Calculator to APPROXIMATE the Values: arctan(-6.24) = -80.9°/-1.412 sin^(-1)(0.2234) = 12.9° arccos(2.4) = NOT IN DOMAIN OF cos^(-1) USE AN INVERSE TRIG FUNCTION TO WRITE θ AS A FUNCTION OF x: θ cosθ = 4/x θ = cos^(-1)(4/x) SOLVING RIGHT TRIANGLES Triangle 1: A = 62.7° a = 7.4 b = 3.8 90 - 27.3 cos 27.3 = a/8.3 sin 27.3 = b/8.3 Triangle 2: A = 47.8° B = 42.2° b = 3.9 sin A = 4.3/5.8 90 - 47.8 cos B = 4.3/5.8 cos 47.8 = b/5.8 Alternative Calculation for b in Triangle 2: 4.3^2 + b^2 = 5.8^2 b^2 = 5.8^2 - 4.3^2 b = sqrt(5.8^2 - 4.3^2) LAND BEARINGS Trigonometry and Bearings In surveying and navigation, directions can be given in terms of bearings. A bearing measures the acute angle that a path or line of sight makes with a fixed north-south line, as shown in Figure 4.82. For instance, the bearing S 35° E in Figure 4.82 means 35 degrees east of south. three diagrams showing different bearings AIR NAVIGATION BEARINGS Study Tip: In air navigation, bearings are measured in degrees clockwise from north. Examples of air navigation bearings are shown below. diagram showing air navigation bearings 36. NAVIGATION A jet leaves Reno, Nevada and is headed toward Miami, Florida at a bearing of 100°. The distance between the two cities is approximately 2472 miles. (a) How far north and how far west is Reno relative to Miami? (b) If the jet is to return directly to Reno from Miami, at what bearing should it travel? diagram showing the flight path between Reno and Miami Solution: (a) cos(10°) = x/2472 => x = 2434.4 miles sin(10°) = y/2472 => y = 429.3 miles (b) 280° A jet leaves Salt Lake City, Utah and is headed toward San Diego, California at a bearing of 215°. The distance between the two cities is approximately 626 miles. a. How far South and how far West is San Diego relative to Salt Lake City? b. If the jet is to return directly to Salt Lake from San Diego at what bearing should it travel? 1 coordinate plane with a line segment representing the flight path Calculations: a. cos(55°) = x/626 => x = 359.1 miles sin(55°) = y/626 => y = 512.8 miles b. 215° - 180° = 35°