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Sagot :
Using trigonometric identities, it is found that the exact value of the secant of the angle is given by:
c. [tex]\sec{\theta} = - \sqrt{5}[/tex]
How is the tangent related to the secant?
According to the following identity:
[tex]\sec^2{\theta} = 1 + \tan^2{\theta}[/tex]
The tangent is the inverse of the cotangent, hence in this problem, we have that:
[tex]\tan{\theta} = -2[/tex]
Then, the secant is given as follows:
[tex]\sec^2{\theta} = 1 + (-2)^2[/tex]
[tex]\sec^2{\theta} = 5[/tex]
[tex]\sec{\theta} = \pm \sqrt{5}[/tex]
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. [tex]\sec{\theta} = - \sqrt{5}[/tex]
More can be learned about trigonometric identities at https://brainly.com/question/24496175
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