Mathematics: Find all values of theta if theta is in the interval [0degrees,360degrees) and has the given function value sec theta= -2

Find all values of theta if theta is in the interval

emilyarvin

17.03.2022

$\theta = 120, 240$ , in degrees

Step-by-step explanation:

The secant of an angle is given by:

$\sec{\theta} = \frac{1}{\cos{\theta}}$

In this question:

$\sec{\theta} = -2$

$\frac{1}{\cos{\theta}} = -2$

$-2\cos{\theta} = 1$

$\cos{\theta} = -\frac{1}{2}$

In the first quadrant, the angle that has cosine of 1/2 is 60º.

The cosine is negative in the second and in the third quadrant.

The equivalent angle to 60º in the second quadrant is of 180º - 60º = 120º.

The equivalent angle to 60º in the third quadrant is of 180º + 60º = 240º

So the values of $\theta$ in the interval are:

$\theta = 120, 240$ , in degrees

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