# sin (a)  = 0.23 what is cos (a)

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

We have sin a = 0.23

To find cos a, use the relation (cos a) = sqrt [ 1 - (sin a)^2]

=> cos a = sqrt [1 - (0.23)^2]

=> cos a = sqrt 0.9471

=> cos a = 0.9731 and -0.9731

The required value of cos a = 0.9731 and -0.9731

hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted on

Given that sin(a) = 0.23

We need to find the value of cos(a)

We can use two different methods.

First, using the calculator we will find the value of angle a.

==> a= arcsin 0.23 = 13.2971 degree

Now we will find the cos (a) = cos( 13.2971)

==> cos a =+- 0.9732

Method (2)

We use the identity sin^2 x+ cos^2 x = 1

==> cosa = +-sqrt( 1- 0.23^2) = +-0.9732

Then the value of cos a= +- 0.9732

tonys538 | Student, Undergraduate | (Level 1) Valedictorian

Posted on

The value of cos a has to be determined given that sin a  = 0.23.

Use the relation `sin^2x + cos^2x = ` 1 which holds for all values of x.

`cos^2 a = 1 - sin^2 a`

`cos^2 a = 1 - (0.23)^2`

`cos^2a = 0.9471`

`cos a = +-sqrt (0.9471)`

For each value of sin a there are two values of cos a, as these functions do not have a linear graph.