Given tanu= -1/3 and sinu <0, find sin(u/2)

Question

if 0 is less than or equal to u < 2 pie

I think its a right triangle in fourth quadrant with the point (3,-1) (hypotenuse equals square root of ten) but I'm brain dead and can't find u or any solutions.

Answer 1

I assume you want to solve for u, not a triangle. Tan u is negative in the second and fourth quadrant, and sie u is negative in the third and fourth, therefore you are correct that u must be in the fourth quadrant. The reference angle (which it makes with the +x axis is arctan 1/3.) You are correct that a line between (3, -1) and the origin will make an agle u with the x axis. That angle is 18.435 degrees and the angle u is 341.565 degrees