교과서 질문
Find the reference angle for each angle.
5π/4
591
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Ch. 1 - Angles and the Trigonometric Functions
Blitzer3rd EditionTrigonometryISBN: 9780137316601
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Table of contents
1장, 문제 43
In Exercises 39–48, use a calculator to find the value of the trigonometric function to four decimal places.
csc 17°
검증된 단계별 안내1
Recall that the cosecant function is the reciprocal of the sine function. This means that \(\csc \theta = \frac{1}{\sin \theta}\).
Identify the angle given in the problem, which is \(17^\circ\).
Use a calculator to find the sine of \(17^\circ\). Make sure your calculator is set to degree mode before calculating \(\sin 17^\circ\).
Calculate the reciprocal of the sine value obtained: \(\csc 17^\circ = \frac{1}{\sin 17^\circ}\).
Round the result to four decimal places as requested.
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.
Reciprocal Trigonometric Functions
The cosecant (csc) function is the reciprocal of the sine function, defined as csc θ = 1/sin θ. Understanding this relationship allows you to find csc values by first calculating sine values and then taking their reciprocals.
추천 영상:
6:04
Introduction to Trigonometric Functions
Using a Calculator for Trigonometric Values
Calculators can directly compute sine values for given angles in degrees or radians. To find csc 17°, first calculate sin 17° using the calculator, then take the reciprocal to get csc 17°, ensuring the calculator is set to degree mode.
추천 영상:
4:45How to Use a Calculator for Trig Functions
Rounding and Precision in Trigonometric Calculations
When reporting trigonometric values, it is important to round the result to the specified number of decimal places, here four. This ensures consistency and accuracy in answers, especially when using approximate decimal values from calculators.
추천 영상:
4:45How to Use a Calculator for Trig Functions
관련 실천
교과서 질문
In Exercises 39–48, use a calculator to find the value of the trigonometric function to four decimal places.
cos 𝜋/10
651
views
교과서 질문
In Exercises 41–56, use the circle shown in the rectangular coordinate system to draw each angle in standard position. State the quadrant in which the angle lies. When an angle's measure is given in radians, work the exercise without converting to degrees.
3𝜋/4
681
views
교과서 질문
In Exercises 33–42, let sin t = a, cos t = b, and tan t = c. Write each expression in terms of a, b, and c.
cos t + cos(t + 1000𝜋) - tan t - tan(t + 999𝜋) - sin t + 4 sin(t - 1000𝜋)
574
views
교과서 질문
In Exercises 41–56, use the circle shown in the rectangular coordinate system to draw each angle in standard position. State the quadrant in which the angle lies. When an angle's measure is given in radians, work the exercise without converting to degrees.
7𝜋/4
617
views
교과서 질문
In Exercises 44–48, find the reference angle for each angle.
265°
726
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