Question

In which quadrant does θ lie if the following statements are true cos θ 0 and tan θ 0 Cosθ 0 and Tanθ 0?

Answer 1

Answer:

• cot θ > 0, so tan θ >0 ie tan θ is positive. cos θ > 0 , ie cos θ is positive. ALL trig ratios are positive in the 1st quadrant. Hence,θ is in the 1st quadrant.

Answer 2

Answer:

cosθ > 0 , tanθ > 0 ; I Quadrant

cosθ < 0 , tanθ < 0 ; II Quadrant

cosθ < 0 , tanθ > 0 ; III Quadrant

cosθ > 0 , tanθ < 0 ; IV Quadrant

Step-by-step explanation:

Taking all the cases into consideration -

Case - 1

cosθ > 0 , tanθ > 0

we know that cos is positive in the I and IV quadrants.

also, tan is positive in the I and III quadrants.

So taking common it will be in the I quadrant.

Case - 2

cosθ < 0 , tanθ < 0

we know that cos is negative in the II and III quadrants.

also, tan is negative in the II and IV quadrants.

So taking common it will be in the II quadrant.

Case - 3

cosθ < 0 , tanθ > 0

we know that cos is negative in the II and III quadrants.

also, tan is positive in the I and III quadrants.

So taking common it will be in the III quadrant.

Case - 4

cosθ > 0 , tanθ < 0

we know that cos is positive in the I and IV quadrants.

also, tan is negative in the II and IV quadrants.

So taking common it will be in the IV quadrant.

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