교과서 질문
In Exercises 9–16, use the given triangles to evaluate each expression. If necessary, express the value without a square root in the denominator by rationalizing the denominator.
sin 𝜋/4 - cos 𝜋/4
636
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Ch. 1 - Angles and the Trigonometric Functions
Blitzer3rd EditionTrigonometryISBN: 9780137316601
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Table of contents
1장, 문제 14
In Exercises 13–17, find a positive angle less than 360° or 2𝜋 that is coterminal with the given angle. -445°
검증된 단계별 안내1
Understand that two angles are coterminal if they differ by a full rotation, which is 360° in degrees or \(2\pi\) in radians.
Since the given angle is \(-445^\circ\), we want to find a positive angle \(\theta\) such that \(\theta = -445^\circ + 360^\circ \times k\), where \(k\) is an integer.
Choose an integer \(k\) that makes \(\theta\) positive and less than 360°. Start by adding 360° once: \(-445^\circ + 360^\circ = -85^\circ\), which is still negative.
Add 360° again: \(-445^\circ + 2 \times 360^\circ = -445^\circ + 720^\circ = 275^\circ\), which is positive and less than 360°.
Therefore, \(275^\circ\) is a positive angle less than 360° that is coterminal with \(-445^\circ\).
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주요 개념
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Coterminal Angles
Coterminal angles are angles that share the same initial and terminal sides but differ by full rotations of 360° or 2π radians. To find a coterminal angle, you add or subtract multiples of 360° (or 2π) until the angle lies within the desired range.
추천 영상:
04:46
Coterminal Angles
Angle Measurement in Degrees
Angles can be measured in degrees, where one full rotation equals 360°. Understanding how to manipulate angles in degrees, including adding or subtracting 360°, is essential for finding equivalent angles within a specified interval.
추천 영상:
5:31Reference Angles on the Unit Circle
Positive Angle Restriction
When asked to find a positive angle less than 360°, you must adjust the given angle by adding 360° repeatedly until the result is positive and less than 360°. This ensures the angle is expressed within the standard range for one full rotation.
추천 영상:
05:50Drawing Angles in Standard Position
관련 실천
교과서 질문
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
Use the (x,y) coordinates in the figure to find the value of each trigonometric function at the indicated real number, t, or state that the expression is undefined.
<IMAGE>
In Exercises 11–18, continue to refer to the figure at the bottom of the previous page.
sec 11𝜋/6
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교과서 질문
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
Use the (x,y) coordinates in the figure to find the value of each trigonometric function at the indicated real number, t, or state that the expression is undefined.
In Exercises 11–18, continue to refer to the figure at the bottom of the previous page.
cos 3𝜋/2
2227
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교과서 질문
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
Use the (x,y) coordinates in the figure to find the value of each trigonometric function at the indicated real number, t, or state that the expression is undefined.
In Exercises 11–18, continue to refer to the figure at the bottom of the previous page.
sec 5𝜋/3
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교과서 질문
Use the given triangles to evaluate each expression. If necessary, express the value without a square root in the denominator by rationalizing the denominator.
<IMAGE>
tan 𝜋/3
425
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교과서 질문
The unit circle has been divided into twelve equal arcs, corresponding to t-values of
0, 𝜋/6, 𝜋/3, 𝜋/2, 2𝜋/3, 5𝜋/6, 𝜋, 7𝜋/6, 4𝜋/3, 3𝜋/2, 5𝜋/3, 11𝜋/6, and 2𝜋
Use the (x,y) coordinates in the figure to find the value of each trigonometric function at the indicated real number, t, or state that the expression is undefined.
<IMAGE>
sin 3𝜋/2
542
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