Trigonometry : Understand the Signs of the 6 Trigonometric Functions in Each Quadrant

Study concepts, example questions & explanations for Trigonometry

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Example Question #11 : Understand The Signs Of The 6 Trigonometric Functions In Each Quadrant

Which of the following is equivalent to tan 315?

Possible Answers:

Correct answer:

Explanation:

When drawn from the origin, a line 315 degrees counterclockwise from the positive x-axis lies in quadrant IV. Tangent is defined as the ratio between the opposite and adjacent sides of a triangle. A right triangle can be drawn in quadrant IV composed of any point on that line, the origin and a point on the x-axis. The opposite side of this triangle lies below the x-axis, and is therefore represented by a negative number. The adjacent side of this triangle lies on the positive x-axis, and is therefore positive. Since the opposite side and hypotenuse have opposite signs, the fraction O/A is negative. Since the triangle formed is a 45-45-90 triangle, the opposite and adjacent side lengths have the same absolute value, so the fraction O/A has an absolute value of 1. Therefore, tan 315 = -1.

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