If sin(x) = − 12 37 and x is in quadrant III, find the exact values of the expressions without solving for x. a. sin(x/2) b. cos(x/2) c. tan(x/2)

Answer 1

Hi Bella, when You get the value of Sin(x), then you can find easily the values of cos(x) and tan(x) as well .

and Sin will be negative in 3rd and 4th quadrant , as Cos will be nagative 2nd and 3rd Quadrant .

so from the above problem it is given Sin (X) = -12/37 , therefore Cos(X) equal to -35/37 .....as X in the 3rd Quadrant Cos will be negative too..

tan(X)= 12/35 as from the formula we know Tan(x) = sin(x) / Cos(x) .....and tan will be positive in 3rd Quadrant.

Now from the half angle formula , we know Sin(x/2) = ±√( 1- cosx) / 2

Cos(x/2) = ±√( 1+ cosx) /2

tan(x/2 ) = ( 1-cosx )/ sinx

now we got all those values fo sinx , cosx and tanx , substitute those values in above formulas you will get the answers.

Answer 2

The missing adjacent side is 35 by pythagorean.

Sine is -12/37

Ccosine is -35/37 as cosine is negative in quadrant 3

Tangent is 12/35

You can now use the half angle formulas