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In which quadrant does θ lie if the following statements are true:secant, theta, is greater than, 0, and , cosecant, theta, is less than, 0secθ>0 and cscθ<0

Question

In which quadrant does θ lie if the following statements are true:secant, theta, is greater than, 0, and , cosecant, theta, is less than, 0secθ>0 and cscθ<0

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Solution

The secant function, sec(θ), is positive in the first and fourth quadrants. The cosecant function, csc(θ), is negative in the third and fourth quadrants. Therefore, if sec(θ) > 0 and csc(θ) < 0, then θ must lie in the fourth quadrant.

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