If the sine of 30 degrees is 1/2, what is the cosine of 60 degrees?

The relationship between sine and cosine in trigonometry can often lead to some interesting insights. In fact, sine and cosine of complementary angles are equal to each other. In this case, you mentioned that sin(30°) = 1/2. This is a well-known sine value that corresponds to a 30-degree angle.

Now, let’s understand the cosine part. The cosine of 60 degrees (cos(60°)) is directly related to the sine of 30 degrees. Since 30 degrees and 60 degrees are complementary angles, we can use the identity:

cos(θ) = sin(90° – θ)

Applying this identity here:

cos(60°) = sin(90° - 60°) = sin(30°)

As we know from your question, sin(30°) = 1/2. Hence:

cos(60°) = 1/2

To summarize, cos(60°) = 1/2. This demonstrates a fundamental concept in trigonometry that the sine and cosine of complementary angles can be directly related, making it easier to connect these values!