sin (a) = 0.23 what is cos (a)
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
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
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
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.