교과서 질문
In Exercises 17–20, θ is an acute angle and sin θ and cos θ are given. Use identities to find tan θ, csc θ, sec θ, and cot θ. Where necessary, rationalize denominators.sin θ = 3/5, cos θ = 4/5
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Ch. 1 - Angles and the Trigonometric Functions
Blitzer3rd EditionTrigonometryISBN: 9780137316601
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Table of contents
1장, 문제 16
In Exercises 5–18, the unit circle has been divided into twelve equal arcs, corresponding to t-values of0, 𝜋, 𝜋, 𝜋, 2𝜋, 5𝜋, 𝜋, 7𝜋, 4𝜋, 3𝜋, 5𝜋, 11𝜋, and 2𝜋.6 3 2 3 6 6 3 2 3 6Use 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
검증된 단계별 안내1
Identify the angle \( \frac{3\pi}{2} \) on the unit circle.
Locate the corresponding point on the unit circle for \( \frac{3\pi}{2} \).
Observe that the point at \( \frac{3\pi}{2} \) is \((0, -1)\).
Recall that the cosine of an angle in the unit circle is the x-coordinate of the corresponding point.
Conclude that \( \cos \frac{3\pi}{2} \) is the x-coordinate of the point \((0, -1)\).
비슷한 문제에 대한 검증된 영상 답변:
이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.
영상 길이:
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주요 개념
질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.
Unit Circle
The unit circle is a circle with a radius of one centered at the origin of a coordinate plane. It is used to define trigonometric functions for all real numbers. The coordinates of points on the unit circle correspond to the cosine and sine values of angles measured in radians, allowing for easy calculation of these functions.
추천 영상:
06:11
Introduction to the Unit Circle
Trigonometric Functions
Trigonometric functions, such as sine, cosine, and tangent, relate the angles of a triangle to the lengths of its sides. On the unit circle, the cosine of an angle corresponds to the x-coordinate, while the sine corresponds to the y-coordinate of the point on the circle. Understanding these functions is essential for solving problems involving angles and their relationships.
추천 영상:
6:04Introduction to Trigonometric Functions
Radians
Radians are a unit of angular measure used in mathematics, where one radian is the angle subtended at the center of a circle by an arc equal in length to the radius of the circle. The unit circle divides the circle into radians, making it easier to work with angles in trigonometric functions. For example, 3π/2 radians corresponds to 270 degrees, which is a key angle in trigonometry.
추천 영상:
5:04Converting between Degrees & Radians
관련 실천
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
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교과서 질문
In Exercises 13–17, find a positive angle less than 360° or 2𝜋 that is coterminal with the given angle. -445°
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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.
tan 𝜋/4 + csc 𝜋/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 of0, 𝜋, 𝜋, 𝜋, 2𝜋, 5𝜋, 𝜋, 7𝜋, 4𝜋, 3𝜋, 5𝜋, 11𝜋, and 2𝜋.6 3 2 3 6 6 3 2 3 6Use 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.tan 3𝜋/2
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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.
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sin 3𝜋/2
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