# HOW TO FIND VALUES OF TRIGONOMETRIC FUNCTIONS OF ANY ANGLE

The following steps will be useful to find the value of trigonometric functions for any angle.

Step 1 :

To find the value of any trigonometric angles, first we have to write the given angles in any one of the following forms.

 (90 + θ)(90 - θ) (180 + θ) (180 - θ) (270 + θ)(270 - θ) (360 + θ)(360 - θ)

Note :

If the given angle measures more than 360 degree, we have to divide it by 360 and write the remainder in one of the above forms.

Step 2 :

If we write the given angles in the form (90 + θ), (90 - θ), (270 + θ) or (270 - θ), we have to convert the given trigonometric ratios as follows.

sin θ  <---> cos θ

cosec θ  <---> sec θ

tan θ  <---> cot θ

Note :

We have a advantage for cos and sec functions.

That is,

cos ( - θ)  =  cos θ     and    sec (-θ)  =  sec θ

But for other trigonometric ratios,

 sin (-θ)  = - sin θ cosec (-θ) = -cosec θ tan (-θ) = -tan θcot (-θ) = -cot θ

## Values of Trigonometric Angles

 θ 0° 30° 45° 60° 90° sin θ 0 1/2 1/√2 √3/2 1 cos θ 1 √3/2 1/√2 1/2 0 tan θ 0 1/√3 1 √3 ∞

## Practice Problems

Problem 1 :

Find the value of sin 480°.

Solution :

 sin 480° =  sin 120°  =  sin (90 + 30)=  cos 30120° lies in 2nd quadrant. For sin and cosec, we will have positive =  √3/2

So, the value of sin 480° is √3/2.

Problem 2 :

Find the value of sin (-1110°).

Solution :

 sin (-1110°)  =  -sin 1110°  =  -sin 3030° lies in 1st quadrant. For all trigonometric ratios, weh ave positive.=  -1/2

So, the value of sin (-1110°) is -1/√2.

Problem 3 :

Find the value of cos 300°.

Solution :

cos 300°  =  cos (270 + 30)

300° lies in 4th quadrant. For cos and sec, we will have positive.

=  sin 30

=  1/2

So, the value of cos 300° is 1/2.

Problem 4 :

Find the value of tan 1050°.

Solution :

 tan 1050°  =  tan 330  =  tan (270 + 60)=  -cot 60300° lies in 4th quadrant. For cos and sec, we will have positive.=  -1/√3

So, the value of tan 1050° is  -1/√3.

Problem 4 :

Find the value of cot 660°.

Solution :

 tan 660°  =  tan 300  =  tan (270 + 30)=  -cot 30300° lies in 4th quadrant. For cos and sec, we will have positive.=  -√3

So, the value of cot 660° is -√3.

Problem 4 :

Find the value of cot 19π/3.

Solution :

cot 19π/3  =  cot (6π + π/3)

=  cot  π/3

=  √3

Problem 4 :

Find the value of sin (-11π/3).

Solution :

sin (-11π/3)  =  -sin (4π - π/3)

=  sin π/3

√3/2

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