Exact Value 2.11.

Question

Given that sinθ= -5/13,  pi<θ<3pi/2, using the angle formula for sine and tangent, find the exact value of

 

(a) sin θ/2

 

 

(b) tan  θ/2

 

Please show ALL steps and give Final Solution.

Answer 1

Your angle theta is in the third quadrant.  So cos θ must be -12/13 (because of Pythagorean identity;

remember 5-12-13 triangles?).

 

Now use the formula for half angle, and assign the sign + to the result, for sin (½θ)--because the half angle will be in quadrant two.

 

Et cetera...