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xz_007 [3.2K]
3 years ago
7

Find all values of theta if theta is in the interval [0degrees,360degrees) and has the given function value

Mathematics
1 answer:
Mekhanik [1.2K]3 years ago
6 0

Answer:

\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

So

\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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