Question

Select the correct answer.
Consider this equation.
cos(8) = -
If 8 is an angle in quadrant II, what is the value of tanê)?
ОА.
15
8
ов. 15
ос. -
✓15
8
OD. 15

Answer 1

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

B. $-\frac{\sqrt{15}}{7}$

What is the tangent of an angle?

The tangent of an angle is given by it's sine divided by it's cosine, that is:

$\tan{\theta} = \frac{\sin{\theta}}{\cos{\theta}}$

In this problem, we have that:

$\cos{\theta} = -\frac{7}{8}$

The following identity is applied:

$\sin^2{\theta} + \cos^2{\theta} = 1$

Then:

$\sin^2{\theta} + \left(-\frac{7}{8}\right)^2 = 1$

$\sin^2{\theta} + \frac{49}{64} = 1$

$\sin^2{\theta} = \frac{15}{64}$

$\sin{\theta} = \pm \frac{\sqrt{15}}{8}$

Since it is on the second quadrant, it is positive, hence:

$\sin{\theta} = \frac{\sqrt{15}}{8}$

Applying the tangent equation:

$\tan{\theta} = \frac{\sin{\theta}}{\cos{\theta}}$

$\tan{\theta} = \frac{\frac{\sqrt{15}}{8}}{-\frac{7}{8}}$

$\tan{\theta} = -\frac{\sqrt{15}}{7}$

More can be learned about trigonometric identities at https://brainly.com/question/22591162