In Quadrant I of the unit circle, what are the signs of Sin, Cos, and Tan?

In Quadrant I of the unit circle, what are the signs of Sin, Cos, and Tan?

• A. Sin = -, Cos = +, Tan = -
• B. Sin = +, Cos = -, Tan = +
• C. Sin = +, Cos = +, Tan = +
• D. Sin = -, Cos = -, Tan = -

Answer: (C)

In Quadrant I of the unit circle, both the sine and cosine functions are positive because this quadrant represents angles between 0 and 90 degrees (or 0 and π/2 radians). Specifically, sine corresponds to the y-coordinate and cosine to the x-coordinate of a point on the unit circle, and both coordinates are positive in this quadrant. Furthermore, the tangent function, which is the ratio of sine to cosine (tan = sin/cos), is also positive since it is the ratio of two positive values. Thus, in Quadrant I, all three functions—sine, cosine, and tangent—are positive, making the given answer correct. This aligns with the fundamental properties of trigonometric functions relative to the four quadrants of the circle, where the signs of these functions vary depending on the quadrant in which the angle lies.

In Quadrant I of the unit circle, both the sine and cosine functions are positive because this quadrant represents angles between 0 and 90 degrees (or 0 and π/2 radians). Specifically, sine corresponds to the y-coordinate and cosine to the x-coordinate of a point on the unit circle, and both coordinates are positive in this quadrant.

Furthermore, the tangent function, which is the ratio of sine to cosine (tan = sin/cos), is also positive since it is the ratio of two positive values. Thus, in Quadrant I, all three functions—sine, cosine, and tangent—are positive, making the given answer correct.

This aligns with the fundamental properties of trigonometric functions relative to the four quadrants of the circle, where the signs of these functions vary depending on the quadrant in which the angle lies.