How do you evaluate sin(arccos 3/4)?

2 Answers
Jun 15, 2018

sin(arccos(3/4))=sqrt7/4

Explanation:

We know that,

color(orange)((A) sin ( arc sinx)=x , where , x in [-1,1]

Let ,

m=sin(color(blue)(arccos(3/4)))...to(1)

We know that,

color(red)(arccosx=arcsin(sqrt(1-x^2))

:.arccos(3/4)=arcsin(sqrt(1-9/16))

=>color(blue)(arccos(3/4)=arcsin(sqrt7/4)

From (1) . we have

m=sin(color(blue)(arcsin(sqrt7/4)))...tocolor(orange)( Apply(A)

=>m=sqrt7/4~~0.66

i.e.sin(arccos(3/4))=sqrt7/4

Jun 16, 2018

+- 0.66

Explanation:

cos x = 3/4
Calculator and unit circle -->
arc x = +- 41^@41

a. sin (41^@41) = 0.66
b. sin (-41^@41) = - 0.66