What are the signs of Sin, Cos, and Tan in Quadrant IV?

In Quadrant IV, the signs of the trigonometric functions are determined by the position of the angle relative to the unit circle. The angles in this quadrant range from 270° to 360° (or from 3π/2 to 2π radians).

In this quadrant, the sine function corresponds to the y-coordinate of a point on the unit circle. Since the y-coordinates are negative in Quadrant IV, the sine of any angle in this quadrant will be negative.

The cosine function corresponds to the x-coordinate. The x-coordinates are positive in Quadrant IV, resulting in a positive value for the cosine function.

Tangent, which is the ratio of sine to cosine (tan = sin/cos), inherits the signs of those functions. Since sine is negative and cosine is positive in this quadrant, tangent will also be negative.

Thus, in Quadrant IV:

• Sine is negative,

• Cosine is positive,

• Tangent is negative.

This corresponds to the choice that indicates sine is negative, cosine is positive, and tangent is negative. Understanding these relationships helps clarify the behavior of trigonometric functions in different quadrants, reinforcing the concept of the unit circle and the coordinate system.