What is the equivalent angle of $$-1080\text{°}$$ in the range of 0° to 360°?

The equivalent angle is $$-1080\text{°} + 3 \times 360\text{°} = -1080\text{°} + 1080\text{°} = 0\text{°}$$ , which is a quadrantal angle.

What is the equivalent angle of $$\frac{27\text{π}}{4}$$ in the range of 0 to 2π?

The equivalent angle is $$\frac{27\text{π}}{4} - 6\text{π} = \frac{27\text{π}}{4} - \frac{24\text{π}}{4} = \frac{3\text{π}}{4}$$ , which is in Quadrant II.

What is the equivalent angle of $$-\frac{8\text{π}}{3}$$ in the range of 0 to 2π?

The equivalent angle is $$-\frac{8\text{π}}{3} + 3 \times 2\text{π} = -\frac{8\text{π}}{3} + \frac{18\text{π}}{3} = \frac{10\text{π}}{3}$$ , which is in Quadrant III.

What is the significance of quadrantal angles?

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.

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

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.

How can you convert an angle from degrees to radians?

To convert an angle from degrees to radians, multiply the degree measure by $$\frac{\text{π}}{180}$$ . For example, to convert 180° to radians: $$180 \times \frac{\text{π}}{180} = \text{π}$$ .

What is the formula for finding the reference angle?

The reference angle is found by taking the absolute value of the angle's measure and subtracting it from the nearest x-axis angle (0°, 90°, 180°, or 270°). For example, for an angle in Quadrant II, the reference angle is $$180° - \theta$$ .

What is the unit circle and its significance in trigonometry?

The unit circle is a circle with a radius of 1 centered at the origin of the coordinate plane. It is significant in trigonometry because it provides a geometric representation of the sine, cosine, and tangent functions, allowing for easy calculation of these values for various angles.

What is the periodicity of the sine and cosine functions?

The sine and cosine functions are periodic with a period of 2π, meaning their values repeat every 2π radians (or 360°). This periodicity is essential for understanding the behavior of these functions over different intervals.

What is the periodicity of the tangent function?

The tangent function is periodic with a period of π, meaning its values repeat every π radians (or 180°). This is important for solving trigonometric equations involving tangent.

Final AP Pre-Calculus: Trig Mastery Flashcard Practice Flashcards

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14 questions

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1.

FLASHCARD QUESTION

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.

Tags

CCSS.6.NS.C.6B

2.

FLASHCARD QUESTION

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).

3.

FLASHCARD QUESTION

Front

Back

4.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSF.TF.A.2

5.

FLASHCARD QUESTION

Front

Back

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

Tags

CCSS.HSF.TF.A.2

6.

FLASHCARD QUESTION

Front

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

Back

Tags

CCSS.HSF.TF.A.2

7.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSF.TF.A.2

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