Question

Convert theta=5pi/6 to rectangular form.

Answer 1

To convert theta=5pi/6 to rectangular form, we can use the values of sine and cosine of the angle. The rectangular form is (-sqrt (3)/2, 1/2).

Step-by-step explanation:

To convert theta=5pi/6 to rectangular form, we can use the following steps:

1. First, we need to find the values of sine and cosine for the given angle.
2. We know that sine(theta) = y/r and cosine(theta) = x/r, where r is the radius.
3. Since the angle is theta = 5pi/6, we can find the values of sine and cosine using the unit circle.
4. For theta = 5pi/6, sine(theta) = 1/2 and cosine(theta) = -sqrt (3)/2.
5. Now, we can write the rectangular form of theta as (x, y) = (r*cosine(theta), r*sine(theta)).
6. Substituting the values of sine and cosine, we get (x, y) = (-sqrt (3)/2, 1/2).

Therefore, the rectangular form of theta=5pi/6 is (x, y) = (-sqrt (3)/2, 1/2).