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

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Identify the quadrant in which the angle 84° lies. Since 84° is between 0° and 90°, it is in the first quadrant.

Recall the sign rules for trigonometric functions in each quadrant: In the first quadrant, all trigonometric functions (sine, cosine, tangent, cosecant, secant, cotangent) are positive.

Therefore, for the angle 84°, sine (sin 84°) is positive because sine corresponds to the y-coordinate on the unit circle, which is positive in the first quadrant.

Cosine (cos 84°) is positive because cosine corresponds to the x-coordinate on the unit circle, which is positive in the first quadrant.

Tangent (tan 84°), being the ratio of sine to cosine, is also positive in the first quadrant since both sine and cosine are positive.

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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 in the coordinate plane, which is essential for determining the signs of trigonometric functions.

Quadrants and Sign of Trigonometric Functions

The coordinate plane is divided into four quadrants, each with specific signs for sine, cosine, and tangent. For example, in the first quadrant (0° to 90°), all trigonometric functions are positive. Knowing the quadrant of the angle helps identify the sign of each function.

Evaluating Trigonometric Functions at Specific Angles

To determine the sign of trigonometric functions for a given angle, first find the quadrant of the angle, then apply the sign rules for sine, cosine, and tangent in that quadrant. For 84°, which lies in the first quadrant, sine, cosine, and tangent are all positive.