Solve each problem. See Examples 1 and 2. Flying Distance The bearing from A to C is N 64° W. The bearing from A to B is S 82° W. The bearing from B to C is N 26° E. A plane flying at 350 mph takes 1.8 hr to go from A to B. Find the distance from B to C.
Table of contents
- 0. Review of College Algebra4h 45m
- 1. Measuring Angles40m
- 2. Trigonometric Functions on Right Triangles2h 5m
- 3. Unit Circle1h 19m
- 4. Graphing Trigonometric Functions1h 19m
- 5. Inverse Trigonometric Functions and Basic Trigonometric Equations1h 41m
- 6. Trigonometric Identities and More Equations2h 34m
- 7. Non-Right Triangles1h 38m
- 8. Vectors2h 25m
- 9. Polar Equations2h 5m
- 10. Parametric Equations1h 6m
- 11. Graphing Complex Numbers1h 7m
2. Trigonometric Functions on Right Triangles
Trigonometric Functions on Right Triangles
Problem 31
Textbook Question
Determine the signs of the trigonometric functions of an angle in standard position with the given measure. See Example 2.
178°
Verified step by step guidance1
Identify the quadrant in which the angle 178° lies. Since 178° is between 90° and 180°, it lies in the second quadrant.
Recall the signs of the trigonometric functions in the second quadrant: sine (sin) is positive, cosine (cos) is negative, and tangent (tan) is negative.
Use the reference angle to understand the values better. The reference angle for 178° is calculated as \(180^\circ - 178^\circ = 2^\circ\).
Determine the signs of the reciprocal functions based on the signs of sine, cosine, and tangent: cosecant (csc) has the same sign as sine, secant (sec) has the same sign as cosine, and cotangent (cot) has the same sign as tangent.
Summarize the signs: sin(178°) > 0, cos(178°) < 0, tan(178°) < 0, csc(178°) > 0, sec(178°) < 0, cot(178°) < 0.
Verified video answer for a similar problem:This video solution was recommended by our tutors as helpful for the problem above
Video duration:
2mPlay a video:
0 Comments
Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Standard Position of an Angle
An angle in standard position has its vertex at the origin and its initial side along the positive x-axis. The terminal side rotates counterclockwise for positive angles. Understanding this helps locate the angle's terminal side on the coordinate plane, which is essential for determining the signs of trigonometric functions.
Recommended video:
Drawing Angles in Standard Position
Quadrants and Sign of Trigonometric Functions
The coordinate plane is divided into four quadrants, each determining the sign of sine, cosine, and tangent. For example, in the second quadrant (90° to 180°), sine is positive while cosine and tangent are negative. Knowing the quadrant of the angle helps identify the signs of its trigonometric values.
Recommended video:
Quadratic Formula
Reference Angle
The reference angle is the acute angle formed between the terminal side of the given angle and the x-axis. It helps find the exact values of trigonometric functions by relating them to known angles in the first quadrant, while the quadrant determines the sign. For 178°, the reference angle is 2°.
Recommended video:
Reference Angles on the Unit Circle
Related Videos
Related Practice
Textbook Question
659
views
