Question

If sinx= 5/13, and x is a positive acute angle, find sin (x + 3pi/2)

Answer 1

(All angles in radians)

sin(x)=5/13

cos(x)= + OR - sqroot[1-sin^2(x)]

In this case x is positive so:

cos(x)=sqroot[1-sin^2(x)]

cos(x)=sqroot(1 - 25/169)

cos(x)=sqroot(169/169 - 25/169)

cos(x)=sqroot(144/169)

cos(x)=12/13


sin(3pi/2)= -1

cos(3pi/2)=0


sin(alpha+beta)=sin(alpha)*cos(beta)+cos(alpha)*sin(beta)

sin(x+3pi/2)=sin(x)*cos(x+3pi/2)+cos(x)*sin(x+3pi/2)=

(5/13)*0+(12/13)*(-)1=0 - 12/13= -12/13

sin(x+3pi/2)= -12/13

Answer 2

(x+3pi/2) radians = 270°

Answer 3

Sorry mistake.

3pi/2 radians = 270°