Textbook Question
Find a positive angle less than 2π that is coterminal with 16π 3
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1. Measuring Angles
Angles in Standard Position
1:44 minutesProblem 45
Textbook Question
In Exercises 39β48, use a calculator to find the value of the trigonometric function to four decimal places.
cos π/10
Verified step by step guidance1
Recognize that the problem asks for the value of the cosine function at the angle \( \frac{\pi}{10} \). This angle is in radians.
Recall that \( \pi \) radians is equivalent to 180 degrees, so \( \frac{\pi}{10} \) radians corresponds to \( \frac{180}{10} = 18 \) degrees.
Use a calculator set to radian mode to evaluate \( \cos\left(\frac{\pi}{10}\right) \). Make sure the calculator is in the correct mode (radians) before calculating.
Input the expression \( \cos\left(\frac{\pi}{10}\right) \) into the calculator. This can be done by entering \( \pi \) divided by 10, then applying the cosine function.
Record the value displayed by the calculator and round it to four decimal places as required.
Verified video answer for a similar problem:This video solution was recommended by our tutors as helpful for the problem above
Video duration:
1mKey Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Radian Measure
Radian measure is a way to express angles based on the radius of a circle. One radian is the angle subtended by an arc equal in length to the radius. Understanding radians is essential because trigonometric functions often use radian inputs, such as Ο/10 in this problem.
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Cosine Function
The cosine function relates an angle to the ratio of the adjacent side over the hypotenuse in a right triangle. It is periodic and defined for all real numbers, often evaluated using radians. Calculating cos(Ο/10) requires understanding how cosine behaves and how to use a calculator for precise values.
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Using a Calculator for Trigonometric Values
Calculators can compute trigonometric functions to high precision, but the mode must be set correctly (radians vs degrees). For cos(Ο/10), ensure the calculator is in radian mode, input the value accurately, and round the result to four decimal places as required.
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