Question

Find the exact value of sec(theta) if cot(theta)= -1/2 and the terminal side of theta lies in quadrant ii.

a. sec(theta)= -sqrt(5)/2
b. sec(theta)= sqrt(t)/2
c. sec(theta)= -sqrt(5)
d. sec(theta)= sqrt(5)

Answer 1

Using trigonometric identities, it is found that the exact value of the secant of the angle is given by:

c. $\sec{\theta} = - \sqrt{5}$

How is the tangent related to the secant?

According to the following identity:

$\sec^2{\theta} = 1 + \tan^2{\theta}$

The tangent is the inverse of the cotangent, hence in this problem, we have that:

$\tan{\theta} = -2$

Then, the secant is given as follows:

$\sec^2{\theta} = 1 + (-2)^2$

$\sec^2{\theta} = 5$

$\sec{\theta} = \pm \sqrt{5}$

The angle is in the second quadrant, where the cosine is negative, hence the secant also is and option c is correct, that is:

c. $\sec{\theta} = - \sqrt{5}$

More can be learned about trigonometric identities at https://brainly.com/question/24496175

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