How do you find two solutions of the equations $sec θ = - 2$ $sectheta=-2$ ?

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How do you find two solutions of the equations $sec θ = - 2$ $sectheta=-2$ ?

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Answer 1 · 2017-01-19T12:33:58

Two possible solutions are $θ = 120^{\circ}$ $theta=120^@$ and $θ = 240^{\circ}$ $theta=240^@$

Explanation:

By definition $sec = \frac{hypotenuse}{adjacent side}$ $sec=("hypotenuse")/("adjacent side")$
for a triangle in standard position.

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

The $| hypotenuse | : | adjacent side |$ $abs("hypotenuse"):abs("adjacent side")$ ratio of $2 : 1$ $2:1$
implies one of the common trigonometric reference angles, namely $60^{\circ}$ $60^@$

Since a straight line $= 180^{\circ}$ $=180^@$ , the common solutions follow from the image below:
enter image source here

Adding multiples of $360^{\circ}$ $360^@$ to either of these solutions, would give you further (but equivalent) solutions.

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How do you find two solutions of the equations $sec θ = - 2$ $sectheta=-2$ ?

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

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Explanation:

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How do you find two solutions of the equations $sec θ = - 2$ $sectheta=-2$ ?