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

  1. Trigonometric Ratios
  2. Trigonometric Identities
  3. Complementary Angles In Trigonometry
  4. Values Of Certain Angles
  5. Heights And Distances
  6. Double Angle Formulas
  7. Half Angle Formulas
  8. Compound Angle Formulas
  9. 3A formulas
  10. Compound angles sum and differences
  11. Sum to product forms
  12. Trigonometry Problems Using Identities
  13. Trigonometry Practical Problems




Values Of Certain Angles to trigonometry