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Ch. 1 - Angles and the Trigonometric Functions

Blitzer - Trigonometry 3rd Edition

Blitzer3rd EditionTrigonometryISBN: 9780137316601당신이 사용하는 게 아니라요?교과서 변경

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Blitzer 3rd Edition

Ch. 1 - Angles and the Trigonometric Functions

문제 31

1장, 문제 31

In Exercises 31–38, find a cofunction with the same value as the given expression. sin 7°

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1

Recall the cofunction identity for sine and cosine: \(\sin(\theta) = \cos(90^\circ - \theta)\).

Identify the angle in the given expression: here, \(\theta = 7^\circ\).

Apply the cofunction identity by substituting \(\theta\) with \(7^\circ\) to find the equivalent cosine expression.

Write the cofunction expression as \(\cos(90^\circ - 7^\circ)\).

Simplify the angle inside the cosine function to get \(\cos(83^\circ)\), which is the cofunction with the same value as \(\sin 7^\circ\).

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

영상 길이:

1m

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Cofunction Identity

Cofunction identities relate the trigonometric functions of complementary angles, meaning angles that add up to 90°. For sine and cosine, the identity is sin(θ) = cos(90° - θ). This allows us to express sine values in terms of cosine and vice versa.

추천 영상:

Cofunction Identities

Complementary Angles

Complementary angles are two angles whose measures add up to 90°. Understanding this concept is essential because cofunction identities rely on the relationship between an angle and its complement to find equivalent trigonometric values.

추천 영상:

Intro to Complementary & Supplementary Angles

Trigonometric Function Values

Knowing how to evaluate or manipulate trigonometric functions like sine and cosine is crucial. Recognizing that sin 7° can be rewritten using a cofunction identity helps simplify expressions or solve equations involving trigonometric values.

추천 영상:

Introduction to Trigonometric Functions

관련 실천

교과서 질문

In Exercises 25–32, the unit circle has been divided into eight equal arcs, corresponding to t-values of

0, 𝜋/4, 𝜋/2, 3𝜋/4, 𝜋, 5𝜋/4, 3𝜋/2, 7𝜋/4, and 2𝜋.

a. Use the (x,y) coordinates in the figure to find the value of the trigonometric function.

b. Use periodic properties and your answer from part (a) to find the value of the same trigonometric function at the indicated real number.

cot 15𝜋/2

교과서 질문

In Exercises 23–34, find the exact value of each of the remaining trigonometric functions of θ. tan θ = 4/3, cos θ < 0

교과서 질문

In Exercises 25–32, the unit circle has been divided into eight equal arcs, corresponding to t-values of

0, 𝜋/4, 𝜋/2, 3𝜋/4, 𝜋, 5𝜋/4, 3𝜋/2, 7𝜋/4, and 2𝜋.

a. Use the (x,y) coordinates in the figure to find the value of the trigonometric function.

b. Use periodic properties and your answer from part (a) to find the value of the same trigonometric function at the indicated real number.

<IMAGE>

cot 𝜋/2

교과서 질문

In Exercises 30–32, find the measure of the side of the right triangle whose length is designated by a lowercase letter. Round answers to the nearest whole number.

교과서 질문

Find a cofunction with the same value as the given expression.

sin 19°

교과서 질문

In Exercises 25–32, the unit circle has been divided into eight equal arcs, corresponding to t-values of

0, 𝜋/4, 𝜋/2, 3𝜋/4, 𝜋, 5𝜋/4, 3𝜋/2, 7𝜋/4, and 2𝜋.

a. Use the (x,y) coordinates in the figure to find the value of the trigonometric function.

b. Use periodic properties and your answer from part (a) to find the value of the same trigonometric function at the indicated real number.

<Image>

sin 47𝜋/4