Which trigonometric functions are negative in the fourth (iv) quadrant?

Quadrant is the region enclosed by the intersection of the X-axis and the Y-axis.

Trigonometric functions  sine , tangent , cotangent ,  and cosecant are negative in fourth quadrant.

In first quadrant, all trigonometric function will be positive.

In second quadrant, only sine and cosecant trigonometric function is positive.

In third quadrant, only tangent and cotangent will be positive.

In fourth quadrant, only cosine and secant will be positive . Therefore,  Trigonometric functions  sine , tangent , cotangent ,  and cosecant are negative in fourth quadrant.

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Explanation:

On the unit circle we have some point (x,y) such that x = cos(theta) and y = sin(theta). The sine corresponds to the y coordinate of the point on the circle. Quadrant IV is below the x axis which explains why sine is negative here, since y < 0 here.

Since sine is negative, so is cosecant as this is the reciprocal of sine

csc = 1/sin

In quadrant IV, cosine is positive as x > 0 here. So the ratio tan = sin/cos is going to be negative. We have a negative over a positive when we divide.

Because tangent is negative, so is cotangent.

The only positive functions in Q4 are cosine and secant, which is because sec = 1/cos.

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