# Which quadrant does θ lie, if sin θ > 0 and sec θ < 0?

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#### Explanation

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14
Sep 13, 2016

The angle $\theta$ lies in the second quadrant.

#### Explanation:

The secant function has the same sign as the cosine function. sine is positive in the first and second quadrants while cosine is positive in the first and fourth quadrants i.e cosine (and hence secant) is negative in the second quadrant. Angle $\theta$ lies in the second quadrant.

There is a pseudonym that will help you remember the signs of the three trig functions: sine, cosine and tangent in the 4 quadrants

A ll ----- all sine, cosine & tangent are positive in Quadrant 1

S tudents - only sine is +, cosine & tangent both - in Quadrant 2

T ake -- only tangent is +, sine & cosine are - in Quadrant 3

C alculus - onlt cosine is +, sine and tangent are - in Quadrant 4

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