How do you find two solutions of the equations #sectheta=-2#?

1 Answer
Alan P.
Jan 19, 2017

Two possible solutions are #theta=120^@# and #theta=240^@#

Explanation:

By definition #sec=("hypotenuse")/("adjacent side")#
for a triangle in standard position.

The #"hypotenuse"# is always taken to be positive,
so if #sec(theta)# is negative, the #"adjacent side"# must be on the negative X-axis.

The #abs("hypotenuse"):abs("adjacent side")# ratio of #2:1#
implies one of the common trigonometric reference angles, namely #60^@#

Since a straight line #=180^@#, the common solutions follow from the image below:
enter image source here

Adding multiples of #360^@# to either of these solutions, would give you further (but equivalent) solutions.

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