BuyFind

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805
BuyFind

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

Solutions

Chapter C, Problem 11E
To determine

To calculate:

The value of the exact trigonometric ratio of the given radian angle:

  3π4

Expert Solution

Answer to Problem 11E

The exact trigonometric ration of the 3π4

  sin3π4=12cosec3π4=2cos3π4=12sec3π4=2tan3π4=cot3π4=1

Explanation of Solution

Given information:

  3π4

Formula Used:

Trigonometric ratios are given by the following formula:

  sinθ=yrcosecθ=rycosθ=xrsecθ=rxtanθ=yxcotθ=xy

Calculation:

The given value of radian is 3π4rad . 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:

  πrad=180°1rad=180°π

Now, rewrite the given angle in the standard position:

  3π4rad=3π4×180°π3π4rad=3×45°3π4rad=135°

Thus, the given angle 3π4rad measures angle 135° or it is 34 of the half revolution (180°) from the positive x axis.

This angle is drawn as below:

  Single Variable Calculus: Concepts and Contexts, Enhanced Edition, Chapter C, Problem 11E

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=12cosec3π4=ry=21=2cos3π4=xr=12sec3π4=rx=21=2tan3π4=yx=11=1cot3π4=xy=11=1

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