Question

If   lies in the quadrant IV. What can be the value of cos 

 ?

Answer 1

For sin : First and second are positive Third and Fouth are negative

For cos : first and Fourth are positive, 270°-360°

Answer 2

When Ф lies in quadrant IV the value of cos Ф lies in [0, 1].

Explanation:

Given the angle Ф lies in quadrant IV. we have to find the value of cos Ф

As we know, cos Ф is positive only in first and fourth quadrant i.e when Ф lies in 0<Ф<90 and 270<Ф<360.

Hence, cos Ф is positive when Ф lies in 1st and 4th quadrant.

& cos Ф is negative when Ф lies in 2nd and 3rd quadrant.

As, cosФ range from [-1,1]

but in 4th quadrant [0,1]

Hence, when Ф lies in quadrant IV the value of cos Ф lies in [0, 1].