Trigonometry Calculating Range

Introduction :
In mathematics trigonometry is one of the divisions. Trigonometry is derivative from the word Greek. In trigonometry, mainly study about the right triangle. Angle and side of the triangle is deal is deals with trigonometry.  The spherical trigonometry is major division of the trigonometry.  Interval of the given value (higher value and lower values) is said to be range. In the following we see detailed about trigonometry calculating range.

Range of Trigonometry Function:

The different between input values is said to be range. Range between the smaller value and the higher value.

Sine function:

[-1, 1] is the range of the sine function

Cosine function:

[-1, 1] is range of the cosine function.

Tangent function:

All real number is the range of the tangent function.

Cotangent:

All the real number is range of the cotangent.

Secant function:

Range of secant function is the [-`oo` ,-1] and [1,+`oo` ] is ;

Cosecant function:

The range of cosecant function is [-`oo` , -1] and [1, + `oo` ]

Example1: Trigonometry Calculating Range

Find the range of the given function:

P=13sin`(x+(Pi)/(8))+5`

Solution:

In this problem given function is:

P=13sin`(x+(Pi)/(8))+5`

For

P=sin`theta`

Common range value of the given sin function is:

-1`<=sintheta<=+1`

`theta``(x+(pi)/(8)) `

Substitute the `theta` value.

-1`<=sin(x+(pi)/(8))<=+1`

Multiply 13 from the both sides:

-13`<=13sin(x+(pi)/(8))<=+13`

Adding +5 from both side:

-13+5`<=13sin(x+(pi)/(8)+5)<=+13+5`

-8`<=13sin(x+(pi)/(8)+5)<=+18`

Range of the given problem is [-8, 18]

Example2: Trigonometry Calculating Range

Find the range of the given function:

P = 9sin`(x+(Pi)/(7))+3`

Solution:

In this problem given function is:

P = 9sin`(x+(Pi)/(7))+3`

For P = sin`theta`

Common range value of the given sin function is:

-1`<=sintheta<=+1`

`theta``(x+(pi)/(7)) `

Substitute the `theta` value.

-1`<=sin(x+(pi)/(7))<=+1`

Multiply 9 from the both sides:

-9`<=9sin(x+(pi)/(7))<=+9`

Adding +3 from both side:

-9+3`<=9sin(x+(pi)/(7))+3<=+9+3`

-6`<=9sin(x+(pi)/(7)+3)<=+12`

Range of the given problem is [-6, 12]

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Example3: Trigonometry Calculating Range

Find the range of the given function:

P = 6sin`(x+(Pi)/(4))+2`

Solution:

In this problem given function is:

P = 6sin`(x+(Pi)/(4))+2`

For P = sin`theta`

Common range value of the given sin function is:

-1`<=sintheta<=+1`

`theta``(x+(pi)/(4)) `

Substitute the `theta` value.

-1`<=sin(x+(pi)/(4))<=+1`

Multiply 6 from the both sides:

-6`<=6sin(x+(pi)/(4))<=+6`

Adding +2 from both side:

-6+2`<=6sin(x+(pi)/(4))+2<=+6+2`

-4`<=6sin(x+(pi)/(4))+2<=+8`

Range of the given problem is [-4, 8]