Question #3efc5

2 Answers
Feb 10, 2017

#θ = 90°#, or #180°#, or #270°#.

Explanation:

First, we can factor our a #4cosθ# to get:

#4cosθ(cosθ + 1) = 0#

This means that either #4cosθ = 0 => cosθ = 0#

or #cosθ + 1 = 0 => cosθ = -1#

You can consult the trigonometric circle below to help:

graph{x^2 +y^2 = 1 [-2.5, 2.5, -1.25, 1.25]}

#cosθ# corresponds to the #x# axis. The angle #θ# is measured from the Ox semiaxis, going counterclockwise. Therefore,

#cosθ = 0 => θ = 90°# or #θ = 270°#
#cosθ = -1 => θ = 180°#

So the three possible solutions are

#{90°, 180°, 270°}#

Feb 10, 2017

#theta = 90^o, 180^o and 270^o#

Explanation:

Factor: #4cos theta (cos theta + 1) = 0#

#4 cos theta = 0, and cos theta = -1#

From a trig. circle: #cos theta = 0 # occurs at # 90^o and 270^o#
From a trig. circle: #cos theta = -1 # occurs at # 180^o#