Single Variable Calculus: Concepts and Contexts, Enhanced Edition
4th Edition
ISBN: 9781337687805
Author: James Stewart
Publisher: Cengage Learning
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Chapter C, Problem 11E
To determine
To calculate:
The value of the exact trigonometric ratio of the given radian angle:
3π4
Expert Solution & Answer
Answer to Problem 11E
The exact trigonometric ration of the 3π4
sin3π4=1√2 cosec3π4=√2cos3π4=−1√2 sec3π4=−√2tan3π4=cot3π4=−1
Explanation of Solution
Given information:
3π4
Formula Used:
Trigonometric ratios are given by the following formula:
sinθ=yr cosecθ=r ycosθ=xr secθ=rxtanθ=yx cotθ=xy
Calculation:
The given value of radian is −3π 4 rad . It is negative angle value that means the rotation is measured from the x− axis as clockwise direction.
Know that:
In one full rotation the angle is 2π . And the relation between the degree and radian is shown by below expression:
π rad=180°1 rad=180°π
Now, rewrite the given angle in the standard position:
−3π 4 rad=−3π 4 ×180°π−3π 4 rad=−3×45°−3π 4 rad=−135°
Thus, the given angle −3π 4 rad measures angle −135° or it is 34 of the half revolution (180°) from the positive x− axis.
This angle is drawn as below:
Here, the triangle is fixed at terminal (x,y)=(1,−1) and r=√(−1)2+(1)2=√2
Therefore, trigonometric ratios are given as:
sin3π4=yr=1√2 cosec3π4=r y=√21=√2cos3π4=xr=−1√2 sec3π4=rx=−√21=−√2tan3π4=yx=1−1 =−1 cot3π4=xy=−11=−1
Chapter C Solutions
Single Variable Calculus: Concepts and Contexts, Enhanced Edition
Ch. C - Prob. 1ECh. C - Prob. 2ECh. C - Prob. 3ECh. C - Prob. 4ECh. C - Prob. 5ECh. C - If a circle has radius 10 cm, find the length of...Ch. C - A circle has radius 1.5 m. What angle is subtended...Ch. C - Prob. 8ECh. C - Prob. 9ECh. C - Prob. 10E
Ch. C - Prob. 11ECh. C - Prob. 12ECh. C - Prob. 13ECh. C - Prob. 14ECh. C - Find, correct to five decimal places, the length...Ch. C - Prob. 16ECh. C - Prob. 17ECh. C - Prob. 18ECh. C - Prob. 19ECh. C - Prob. 20ECh. C - Prob. 21ECh. C - Prob. 22ECh. C - Prob. 23ECh. C - Prob. 24ECh. C - Prob. 25ECh. C - Prob. 26ECh. C - Prob. 27ECh. C - Prob. 28ECh. C - Prob. 29ECh. C - Prob. 30ECh. C - Prob. 31ECh. C - Prob. 32ECh. C - Prob. 33ECh. C - Prob. 34ECh. C - Prob. 35ECh. C - Prob. 36ECh. C - Prob. 37ECh. C - Prob. 38ECh. C - Prob. 39ECh. C - Prob. 40ECh. C - Prob. 41ECh. C - Prob. 42ECh. C - Prob. 43ECh. C - Prob. 44ECh. C - Use the addition formula for cosine and the...Ch. C - Prob. 46E
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