Domanda del libro di testo
Identify the quadrant (or possible quadrants) of an angle θ that satisfies the given conditions. See Example 3. cos θ > 0 , sec θ > 0
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Ch. 1 - Trigonometric Functions
Lial12th EditionTrigonometryISBN: 9780136552161, 9780135440780, 9780136881117, 9780135440827, 9780135924891
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TOC.tableOfContents
- Ch. R - Algebra Review381
- Ch. 1 - Trigonometric Functions188
- Ch. 2 - Acute Angles and Right Triangles168
- Ch. 3 - Radian Measure and The Unit Circle155
- Ch. 4 - Graphs of the Circular Functions100
- Ch. 5 - Trigonometric Identities238
- Ch. 6 - Inverse Circular Functions and Trigonometric Equations158
- Ch. 7 - Applications of Trigonometry and Vectors148
- Ch. 8 - Complex Numbers, Polar Equations, and Parametric Equations15
Lial12th EditionTrigonometryISBN: 9780136552161, 9780135440780, 9780136881117, 9780135440827, 9780135924891Non è quello che usi tu?Cambia libro di testo
Capitolo 2, Problema 40
Concept Check Suppose that the point (x, y) is in the indicated quadrant. Determine whether the given ratio is positive or negative. Recall that r = √(x² + y²) .(Hint: Drawing a sketch may help.) II , y/x
Guida verificata passo dopo passo1
Recall that the ratio given is \( \frac{y}{x} \), where \(x\) and \(y\) are the coordinates of a point in the plane.
Identify the signs of \(x\) and \(y\) in Quadrant II. In this quadrant, \(x < 0\) (negative) and \(y > 0\) (positive).
Since \(y\) is positive and \(x\) is negative, the ratio \( \frac{y}{x} \) is a positive number divided by a negative number.
Dividing a positive number by a negative number results in a negative value, so \( \frac{y}{x} < 0 \) in Quadrant II.
Therefore, the ratio \( \frac{y}{x} \) is negative when the point \((x, y)\) lies in Quadrant II.
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Coordinate Plane Quadrants
The coordinate plane is divided into four quadrants, each with specific signs for x and y coordinates. In Quadrant II, x is negative and y is positive. Understanding the sign of coordinates in each quadrant helps determine the sign of ratios like y/x.
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Percorso guidato
6:36
Quadratic Formula
Sign of Ratios in Different Quadrants
The sign of a ratio such as y/x depends on the signs of y and x individually. Since y is positive and x is negative in Quadrant II, the ratio y/x will be negative. This concept is crucial for evaluating trigonometric ratios based on point location.
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Percorso guidato
6:36Quadratic Formula
Distance from Origin (r = √(x² + y²))
The distance r from the origin to the point (x, y) is always positive and is calculated using the Pythagorean theorem. While r is not directly needed to find the sign of y/x, it is fundamental in defining trigonometric functions and understanding the point's position.
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Percorso guidato
04:47Complex Numbers In Polar Form
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Give all six trigonometric function values for each angle θ . Rationalize denominators when applicable.
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Give all six trigonometric function values for each angle θ . Rationalize denominators when applicable.
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