Table of contents

0. Review of College Algebra4h 43m
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

Trigonometry

2. Trigonometric Functions on Right Triangles

Trigonometric Functions on Right Triangles

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1:58 minutes

Problem 28

Textbook Question

Determine the signs of the trigonometric functions of an angle in standard position with the given measure. SeeExample 2. 84°

Verified step by step guidance

Step 1: Understand the problem. We need to determine the signs of the trigonometric functions (sine, cosine, and tangent) for an angle of 84° in standard position.

Step 2: Identify the quadrant. Since 84° is between 0° and 90°, it is in the first quadrant.

Step 3: Recall the signs of trigonometric functions in the first quadrant. In the first quadrant, all trigonometric functions (sine, cosine, and tangent) are positive.

Step 4: Conclude the signs. Therefore, for an angle of 84° in standard position, sine, cosine, and tangent are all positive.

Step 5: Verify understanding. Remember that the first quadrant is where all trigonometric functions are positive, which is consistent with our findings for 84°.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Standard Position of an Angle

An angle is in standard position when its vertex is at the origin of a coordinate system and its initial side lies along the positive x-axis. The angle is measured counterclockwise from the initial side. Understanding this concept is crucial for determining the location of the terminal side of the angle and subsequently the signs of the trigonometric functions.

Quadrants of the Coordinate Plane

The coordinate plane is divided into four quadrants, each defined by the signs of the x and y coordinates. In Quadrant I, both x and y are positive; in Quadrant II, x is negative and y is positive; in Quadrant III, both are negative; and in Quadrant IV, x is positive and y is negative. The quadrant in which the terminal side of the angle lies determines the signs of the sine, cosine, and tangent functions.

Signs of Trigonometric Functions

The signs of the six trigonometric functions (sine, cosine, tangent, cosecant, secant, and cotangent) depend on the quadrant in which the angle's terminal side is located. In Quadrant I, all functions are positive; in Quadrant II, sine and cosecant are positive; in Quadrant III, tangent and cotangent are positive; and in Quadrant IV, cosine and secant are positive. This knowledge is essential for accurately determining the values of these functions for any given angle.