103k views
1 vote
If cos x= -4/5 and pi Please someone can help me?

If cos x= -4/5 and pi Please someone can help me?-example-1

1 Answer

3 votes

Answer:


sin(x+(\pi )/(2)) = (-4)/(5)

Explanation:

Given
cos x = (-4)/(5)

given 'x' lies in
\pi <x<(3\pi )/(2)

we know that sin(A+B) = sin A cos B + cos A sin B


sin(x+(\pi )/(2) ) =
sin x cos((\pi )/(2) )+ cos x sin((\pi )/(2) ) .........................(1)

we will use trigonometry formulas


cos((\pi )/(2)) = 0


sin((\pi )/(2) )=1

sin x is negative in third and fourth quadrant (
\pi <x<(3\pi )/(2))

find sin x value

using trigonometry formulas
sin^(2) x+cos^2 x=1


sin^(2)x = 1 - cos^2 x

=
1-((-4)/(5)))^2


sin^2 x = 1 - (16)/(25)


sin x = \sqrt{(25-16)/(25) }

sin x =
\sqrt{(9)/(25) }


sin x = (3)/(5)

in third and fourth quadrant is negative so sin x=
(-3)/(5)

now equation (1), we get solution


sin(x+(\pi )/(2)) = sin x ( 0 ) + cos x (1)

=
(-4)/(5)

User Thorsten Kranz
by
6.6k points