Question

Seeing that the cosine is positive and the tangent is negative, in which quadrant must theta lie? Find the exact values of the remaining five trigonometric functions. Rationalize denominators and simplify as much as possible. Look carefully at how you simplify cot theta.

Step 1

Here given the value of cos θ and we ned to find the value of tan θ. It is mentioned that tan θ is negative here.

Cos θ is positive in first quadrant and in fourth quadrant and tan θ is positive in first quadrant and negative in fourth quadrant. Since we need positive cos θ and negative tan θ, θ is in fourth uadrant.

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