Solve the problem. Round answers to the nearest tenth if necessary.
-Find tan ϴ, given that cos ϴ = -0.25881905 and ϴ is in quadrant II.
A)-3.7320507
B)3.9910152
C)3.7320507
D)-3.9910152

Question

Quizplus · Accepted Answer

In quadrant II, sine is positive and cosine is negative. The tangent function, which is the ratio of sine to cosine, will be negative. Using the identity $ \tan(\theta) = \frac{\sin(\theta)}{\cos(\theta)} $ and knowing that $ \sin^2(\theta) + \cos^2(\theta) = 1 $, we can find $ \sin(\theta) $ and then $ \tan(\theta) $. Given $ \cos(\theta) = -0.25881905 $, $ \sin(\theta) = \sqrt{1 - \cos^2(\theta)} = \sqrt{1 - (-0.25881905)^2} \approx 0.96592583 $ (positive in quadrant II). Thus, $ \tan(\theta) = \frac{\sin(\theta)}{\cos(\theta)} = \frac{0.96592583}{-0.25881905} \approx -3.7320507 $.

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