Domanda del libro di testo
In Exercises 7–12, find the radian measure of the central angle of a circle of radius r that intercepts an arc of length s. Radius, r: 1 meter Arc Length, s: 600 centimeters
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Ch. 1 - Angles and the Trigonometric Functions
Blitzer3rd EditionTrigonometryISBN: 9780137316601
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Capitolo 1, Problema 12
In Exercises 8–12, draw each angle in standard position. -135°
Guida verificata passo dopo passo1
Understand that an angle in standard position has its vertex at the origin and its initial side along the positive x-axis.
Since the angle given is -135°, recognize that the negative sign indicates a clockwise rotation from the positive x-axis.
Measure 135° clockwise starting from the positive x-axis to locate the terminal side of the angle.
Note that rotating 135° clockwise is equivalent to rotating 225° counterclockwise (since 360° - 135° = 225°), so the terminal side lies in the third quadrant.
Draw the angle by first drawing the initial side along the positive x-axis, then rotating clockwise 135° to draw the terminal side, which will point diagonally in the third quadrant.
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Standard Position of an Angle
An angle is in standard position when its vertex is at the origin of the coordinate plane, and its initial side lies along the positive x-axis. The angle is measured by rotating the initial side to the terminal side, either counterclockwise for positive angles or clockwise for negative angles.
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05:50
Drawing Angles in Standard Position
Measuring Negative Angles
Negative angles are measured by rotating the initial side clockwise from the positive x-axis. For example, a -135° angle means rotating 135 degrees clockwise, which places the terminal side in the third quadrant of the coordinate plane.
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5:31Reference Angles on the Unit Circle
Quadrants and Angle Placement
The coordinate plane is divided into four quadrants, each corresponding to a range of angles. Understanding which quadrant an angle's terminal side lies in helps in accurately drawing and interpreting the angle in standard position.
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6:36Quadratic Formula
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In Exercises 8–13, find the exact value of each expression. Do not use a calculator. sec 22𝜋 3
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In Exercises 5–18, the unit circle has been divided into twelve equal arcs, corresponding to t-values of
0, 𝜋, 𝜋, 𝜋, 2𝜋, 5𝜋, 𝜋, 7𝜋, 4𝜋, 3𝜋, 5𝜋, 11𝜋, and 2𝜋.
6 3 2 3 6 6 3 2 3 6
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In Exercises 11–18, continue to refer to the figure at the bottom of the previous page.
csc 7𝜋/6
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Domanda del libro di testo
In Exercises 9–16, evaluate the trigonometric function at the quadrantal angle, or state that the expression is undefined. csc 𝜋
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<IMAGE>
csc 45°
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In Exercises 8–13, find the exact value of each expression. Do not use a calculator. cot (-8𝜋/3)
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