use a unit circle to find the trigonometric ratios of 240 degree
240 = 180+60
so just use 60 as a reference angle, and then recall that only tan and cot are positive in QIII
To find the trigonometric ratios of 240 degrees using a unit circle, follow these steps:
1. Draw a unit circle on a piece of paper. A unit circle is a circle with a radius of 1 unit.
2. Label the key points on the circle. Start by marking the origin (center of the circle) as point O. The positive x-axis is the right side of the circle and the positive y-axis is the top side of the circle. Label the positive x-axis as "1" and the negative x-axis as "-1". Label the positive y-axis as "i" (which represents the imaginary unit) and the negative y-axis as "-i".
3. Sketch an angle of 240 degrees. To do this, start at the positive x-axis (1) and rotate in a counter-clockwise direction until you reach 240 degrees. Label the endpoint of the angle as point A.
4. Find the x and y coordinates of point A. The x-coordinate represents the cosine of the angle (cos 240), and the y-coordinate represents the sine of the angle (sin 240).
To calculate the coordinates, use the following formulas:
x-coordinate = cos(theta) = cos(240 degrees)
y-coordinate = sin(theta) = sin(240 degrees)
5. Use the position of point A on the unit circle to determine the trigonometric ratios:
- The cosine ratio (cos 240) is equal to the x-coordinate, so cos 240 = x-coordinate.
- The sine ratio (sin 240) is equal to the y-coordinate, so sin 240 = y-coordinate.
- The tangent ratio (tan 240) is equal to the y-coordinate divided by the x-coordinate, so tan 240 = y-coordinate / x-coordinate.
Using the unit circle, you can determine the cos 240, sin 240, and tan 240 values.