## Values Of Certain Angles

On this page we are going to see values of certain angles.All the trigonometric ratios for angle of measures 0°,30°,45°,60° and 90° in the following table.

We can easily memorize all the values given in the above table.First, we have to memorize the angles .That is 0°,30°,45°,60° and 90° then we can just memorize the first row of values for sin θ that is 0,1/2,1/√2,√3/2 and 1.If we write all the above values in reverse we will get the corresponding values for cos θ .To get the values for tan θ we have to divide both the values for sin θ and the cos θ.

To get the values for cosec θ,sec θ and cot θ.We have to use the reciprocal for cosec θ,sec θ and cot θ.

First let us remember the reciprocal formulas.

• sec θ = 1/cos θ
• tan θ = 1/cot θ
• cot θ = 1/tan θ

For example if we need the value of sec 30° we can easily find that using these formulas.Let us consider the following example.

Find the value of sec 30°

sec 30°  =  1/cos 30°

=   1/√3/2

=   1 x 2/√3

=   2/√3

Find the value of cot 30°

cot 30°  =   1/tan 30°

=   1/1/√3

=   1 x √3/1

=    √3

Let us consider the following example problems to understand this topic much better.

Example 1

Evaluate 2 cos² 30° tan² 60° - sec² 45° sin² 45°

Solution:

Cos 30° = √3/2

tan 60° =  √3

sec 45° = 1/ cos 45° = 1/(1/√2) = 1 x (√2/1) = √2

sin 60° =√3/2

=    2 (√3/2)²  (√3)²  -  (√2)² (√3/2)²

=    2 x (3/4) x (3) - 2 (3/4)

=    (9/2) - (3/2)

=    (9-3)/2

=     6/2

=      3

Example 2

Evaluate cosec² 45° cot² 30° + sin² 60° sec² 30°

Solution:

cosec 45° = 1/ sin 45° = 1/(1/√2) = 1 x (√2/1) = √2

cosec 45° =  √2

cot 30° = 1/tan 30° = 1/(1/√3)  = 1 x (√3/1) = √3

cot 30° =  √3

sin 60° = √3/2

sec 30°= 1/cos 30° = 1/(√3/2) = 1 x (2/√3) = 2/√3

=    (√2)²  (√3)²  -  (√3/2)² (2/√3)²

=    2 x 3 - (√3²/2²) (2²/√3²)

=    6 - (3/4) x  (4/3)

=    6 - 1

=    5

These are some examples in the page values of certain angles.

Related Topics

Values Of Certain Angles to trigonometry