Find both solutions between -180 degrees and 180 degrees of the equation tan theta = 1/2

Question

Please explain / show some workings so that I can grasp this concept

Answer 1

1) -180° and 180° are the same. I shall give for all values for 0° to 360°.

2) tan θ = 1/2

θ = 26.565° use a calculator

θ = 206.565° for the angle in QIII

Answer 2

The general procedure for this is described here:

https://www.wyzant.com/resources/answers/696149/find-both-solutions-between-180-degrees-and-180-degrees-of-the-equation-tan

and here:

https://www.wyzant.com/resources/answers/696138/find-both-solutions-between-0-degrees-and-360-degrees-of-the-equation-cos-1

For any problem of this type, start by sketching a picture. since the tan is 1/2, you can plot a line from the origin to the point (2,1) <----this is the standard shorthand for "x = 2, y = 1"

The only other place you can get a tangent of +1/2 is in the 3rd quadrant, where x and y are both negative.

Thus, the angles are theta = arctan(1/2), and then theta + 180 degrees