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 14E
To determine

To calculate:

The remaining trigonometric ratios:

  tanα=2,0<α<π2

Expert Solution

Answer to Problem 14E

The remaining trigonometric ratios are listed as:

  sinα=yr=25cosecα=ry=52cosα=xr=15secα=rx=51cotα=xy=12

Explanation of Solution

Given information:

  tanα=2,0<α<π2

Formula Used:

Trigonometric ratios are given by the following formula:

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

Calculation:

From the given data:

  tanα=yxtanα=2

So, y=2,x=1 the angle is constructed as below:

  Single Variable Calculus: Concepts and Contexts, Enhanced Edition, Chapter C, Problem 14E

Now, find the value of r

  r=x2+y2r=12+42r=5

Therefore, remaining trigonometric ratios are calculated as:

  sinα=yr=25cosecα=ry=52cosα=xr=15secα=rx=51cotα=xy=12

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