To find sine of 60 degrees, we use a special 30-60-90 triangle. In this triangle, the sides are in the ratio 1 to square root of 3 to 2. Sine of 60 degrees equals the opposite side divided by the hypotenuse, which gives us square root of 3 divided by 2.
We can verify this result using the unit circle. At 60 degrees, the point on the unit circle has coordinates one-half and square root of 3 over 2. The y-coordinate represents the sine value, confirming that sine of 60 degrees equals square root of 3 over 2.
Let's go through the calculation step by step. First, we identify that we're working with a 30-60-90 triangle with sides in the ratio 1 to square root of 3 to 2. Second, we apply the sine definition as opposite side over hypotenuse. Third, we substitute the values to get square root of 3 over 2. Finally, our answer is square root of 3 over 2, which is approximately 0.866.
From the same 30-60-90 triangle, we can find all trigonometric values. Sine of 30 degrees is one-half, sine of 60 degrees is square root of 3 over 2. Cosine of 30 degrees is square root of 3 over 2, cosine of 60 degrees is one-half. Tangent of 30 degrees is 1 over square root of 3, and tangent of 60 degrees is square root of 3.
To summarize what we've learned: sine of 60 degrees equals square root of 3 over 2, derived from the 30-60-90 triangle. The unit circle confirms this value. This is a fundamental trigonometric value used in many mathematical applications.