Final AP Pre-Calculus: Trig Mastery Flashcard Practice

Front

What is the definition of a quadrant in the context of the Cartesian coordinate system?

Back

A quadrant is one of the four sections of the Cartesian plane, defined by the x and y axes. Quadrant I is where both x and y are positive, Quadrant II where x is negative and y is positive, Quadrant III where both x and y are negative, and Quadrant IV where x is positive and y is negative.

Front

How do you determine the quadrant of an angle given in degrees?

Back

To determine the quadrant of an angle in degrees, first reduce the angle to its equivalent angle between 0° and 360° by adding or subtracting multiples of 360°. Then, identify the quadrant based on the angle's value: 0° to 90° (Quadrant I), 90° to 180° (Quadrant II), 180° to 270° (Quadrant III), and 270° to 360° (Quadrant IV).

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Back

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Back

This means that the angle theta is in Quadrant II, where tangent is negative and secant (the reciprocal of cosine) is also negative.

Front

How do you find the quadrant of an angle given in radians?

Back

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Front

What is the significance of quadrantal angles?

Back

Quadrantal angles are angles that lie on the axes of the Cartesian plane (0°, 90°, 180°, 270°, and 360°). They are significant because the sine, cosine, and tangent values for these angles are either 0, 1, or -1, which are key values in trigonometric functions.

Front

What is the relationship between the signs of trigonometric functions and the quadrants?

Back

In Quadrant I, all trigonometric functions are positive. In Quadrant II, sine is positive while cosine and tangent are negative. In Quadrant III, tangent is positive while sine and cosine are negative. In Quadrant IV, cosine is positive while sine and tangent are negative.

Front

How can you convert an angle from degrees to radians?

Back