Find the point (x,y) on the unit cirlce that corresponds to the real number t.
t= 11 pie / 6
My answer was (1/2 , -sqrt3/2) but my teacher said it is wrong!
Your teacher asked for the point (x,y).
Did you check your values of sin(5π/6) which corresponds to y, and cos(5π/6) which corresponds to x?
To find the point (x, y) on the unit circle that corresponds to the real number t = 11π/6, we can use the following steps:
Step 1: Convert the angle t from radians to degrees using the formula:
angle in degrees = angle in radians * (180/π)
t (in degrees) = (11π/6) * (180/π) = 330 degrees
Step 2: Plot the angle t = 330 degrees on the unit circle. Start from the positive x-axis and rotate counterclockwise.
Step 3: Determine the coordinates (x, y) by identifying the point where the angle intersects the unit circle. In this case, the point is located in the fourth quadrant, and it has a negative y-coordinate.
Therefore, the correct answer is (x, y) = (1/2, -√3/2).
It is possible that there was a misunderstanding or mistake in the answer provided by your teacher. Feel free to discuss further with them to clarify the confusion.
To find the point (x, y) on the unit circle that corresponds to the real number t, you can use the following steps:
1. Convert the real number t from radians to degrees. In this case, you have t = 11π/6 radians.
2. To convert radians to degrees, use the formula: degrees = radians * (180/π).
degrees = 11π/6 * (180/π)
degrees = 11 * 30
degrees = 330
3. Since the unit circle is centered at the origin with a radius of 1, any point (x, y) on the unit circle can be found by using the trigonometric identities for sine and cosine.
4. To find the x-coordinate (x) of the point, use the cosine function: x = cos(degrees).
x = cos(330)
5. To find the y-coordinate (y) of the point, use the sine function: y = sin(degrees).
y = sin(330)
6. Now, you can calculate the values for x and y:
x = cos(330) ≈ 0.866
y = sin(330) ≈ -0.5
Thus, the correct answer for the point (x, y) on the unit circle that corresponds to t = 11π/6 is approximately (0.866, -0.5).