tanx = root 3 and x is between 180 and 270 find sin(x - 210)

Question

Hi Raquel,

tan(x) = root of 3 it means this angle, x , must be in 1th or 3th quadrant because tangent in these quadrants are positive

you know tan(x) = root 3 will tell you the angle, x , must be 60 and also it must be 3th quadrant so

x = 180 + 60 = 240

now we need to find sin( x - 210).

by plugging 240 in sin ( x- 210 ) we have

sin ( 240 - 210) = sin (30 ) = 1/2

I hope it helps you

Answer 1

Answer: 1/2 = 0.5

sin(A-B)=sinAcosB-sinBcosA

is a general formula that can solve this problem, A=x with 180<x<270, B=210 x=arctan(sqr3) the angle whose tangent is square root of 3 is 60 degrees or 180+60=240 degrees

x-210 = 240-210=30 sin(x-210) = sin(240-210) = sin(30)=1/2 = sin(x-210)

Or you can plug A=240, B=210 into the top equation, a more roundabout longer method, which gives the same answer: 1/2

sin(240-210)=sin240cos210-sin210cos240

=(-sqr3/2)(-sqr3/2)-(-1/2)(-1/2)

=3/4 - 1/4

=1/2