Circle the value of sin of 30 degrees. Is it one over root three, one over two, root three over two, or two over root three?
There is a little way to remember the values for sin and cos of 30 degrees, 45 degrees, and 60 degrees. We write it in table form, and we list the degrees in ascending order. That’s 30, 45, and 60. We then write one, two, three and three, two, one. The denominator of all of these fractions is two.
The final step is to find the square root of the numerator of each fraction. The square root of one though is just one. So we don’t need to write the square root of one for sin of 30 and cos of 60. And we’re done.
Sin of 30 is one-half, sin of 45 is root two over two, and sin of 60 is root three over two. Then we can see that cos of 30 is root three over two, cos of 45 is root two over two, and cos of 60 is one-half.
Notice how the values for sine and cosine are identical for 30, 45, and 60, but they’re in reverse. This means you can actually get away with just learning one set and remembering to reverse for the second set. So we can now see the value of sin 30 using our table. It’s one-half. We circle one-half as shown.