Question #6074d

2 Answers
May 2, 2017

see explanation below

Explanation:

in quadrant 2, the value of #x-axis is -ve while y-axis is +ve and it hypotenuse is +ve value.

sin = y-axis/hypotenuse = +ve value.

cosec = 1/sin = hypotenuse/y-axis = +ve value.

the rest are involve with the #x-axis and become -ve value.

May 2, 2017

It has to do with the signs of the x and y axis in the second quadrant.

We let #sintheta= b/r#, #costheta = a/r# and #tantheta = b/a#, where #a^2 + b^2 = r^2#. Here's why:

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The green triangle is right because side #b# is parallel to the y-axis and the x and y axis are perpendicular to each other. The hypotenuse will always be positive, so it's #a# and #b# that will influence the sign of the ratio.

We have #sintheta = "opposite"/"hypotenuse" = b/r# and #b# will be positive because the y-axis in quadrant II is positive. Therefore, sine will always be positive in quadrant #II#. This also applies to cosecant because #cscx = 1/sinx#.

Hopefully this helps!