Questions: Use the diagram of the unit circle below to answer the following question. Find the sine, cosine, and tangent value for the triangle created with the terminal point Q.

Solution Steps

Point Q lies on the unit circle in the fourth quadrant. Observing the grid, we can see that the x-coordinate of Q is positive and the y-coordinate is negative. The coordinates of Q appear to be at the intersection of x=1/2 and y=-√3/2. Thus, the coordinates of point Q are (1/2, -√3/2).

In a unit circle, the x-coordinate represents the cosine of the angle formed by the terminal point and the positive x-axis, and the y-coordinate represents the sine of that angle. Tangent is defined as the ratio of sine to cosine (sin/cos).

Given the coordinates of Q as (1/2, -√3/2):

• Cosine: The x-coordinate is 1/2, so cos(θ) = 1/2.
• Sine: The y-coordinate is -√3/2, so sin(θ) = -√3/2.
• Tangent: tan(θ) = sin(θ) / cos(θ) = (-√3/2) / (1/2) = -√3

Final Answer