# The remaining trigonometric ratios: sin θ = 3 5 , 0 &lt; θ &lt; π 2

### Single Variable Calculus: Concepts...

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

### Single Variable Calculus: Concepts...

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

#### Solutions

Chapter C, Problem 13E
To determine

## To calculate: The remaining trigonometric ratios:   sinθ=35,   0<θ<π2

Expert Solution

The remaining trigonometric ratios are listed as:

cosecθ=ry=53cosθ=xr=54secθ=rx=45tanθ=yx=34cotθ=xy=43

### Explanation of Solution

Given information:

sinθ=35,0<θ<π2

Formula Used:

Trigonometric ratios are given by the following formula:

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

Calculation:

From the given data:

sinθ=xrsinθ=35

So, x=3,r=5 the angle is constructed as below:

Now, find the value of y

r2=x2+y2(5)2=(3)2+y2y2=259y2=16y=4

Therefore, remaining trigonometric ratios are calculated as:

cosecθ=ry=53cosθ=xr=54secθ=rx=45tanθ=yx=34cotθ=xy=43

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