cos theta = -1/2 what is sin

Answer 1

cos theta = -1/2 what is sin

Step 1. Find out what theta (Θ) is

Step 2. Once you know theta (Θ), you can find the sin of theta (Θ).

Step 1....Cos theta(Θ)= -1/2.....so the inverse function (cos ^-1) of cos will give us theta (Θ) written as.....

inverse cos (cos (Θ)) = inverse cos (-1/2) = theta......

when you evaluate this you get theta (Θ) = 120 degrees

step 2 what is the sin 120 = 0.8660254038 = √3 / 2

Answer 2

cosθ=-.5

θ=120

sinθ120=.86602.............

Answer 3

cosine is adjacent side/hypotenuse = a/h

sine is opposite side/hypotenuse = o/h

a/h=-1/2 is in the 2nd or 3rd quadrant; positive cosines are in the 1st or 4th quadrant

o=sqr(h^2-a^2) = sqr(4-1) = sqr3 = about 1.732

sine of theta = o/h = sqr3/2 if theta is in the 2nd quadrant

but = -sqr3/2 if in the 3rd quadrant

without more info you don't know if it's in the 2nd or 3rd quadrant

theta is either 180 plus or minus 60,

or = 120 degrees or 240 degrees

sin(theta) = either sin(120) or sin(240) = + or - sqr3/2 = about + or - 0.866

actually theta could be 120+2npi degrees or 240 + 2npi degrees where n = any integer, + or -

that's mixing radians and degrees though.

theta = 120 + or -360n degrees where n is any integer

or theta = 2pi/3 + or - 2npi radians

or theta = 240 + or - 360n degrees

or theta = 4pi/3 + or - 2npi radians