This lesson will summarize the trigonometric ratios of special angles taken from lesson #1 to lesson #6. We show you these results here before we move on to more complicated topics.
By special angles, we mean 30 degrees, 45 degrees, and 60 degrees.
These are the angles from the 45-45-90 degrees triangle and the 30-60-90 degrees triangle.
In lesson #1, we saw that tan(45 degrees) = 1In lesson #2 and lesson #4, we saw that sin(45 degrees) = 1 / √(2) = √(2) / 2
Here is the math though showing why 1 / √2 = √2 / 2
Multiply both the numerator and the denominator of 1 / √2 by √2.
(1 × √2) / ( √2 × √2) = (√2) / [√(2 × 2)] = (√2) / √4 = (√2) / 2In lesson #5 and lesson #6, we got the following results:
Some teachers will ask you to memorize the trigonometric ratios of these special angles. Some teachers may not. It is not a bad idea though to know it by heart or be able to reproduce it quickly. Look at the table carefully. Is there some type of pattern or mnemonic that make it easy to reproduce the trigonometric ratios of these special angles?
Notice that for sine, the denominator is always 2. For the numerators, start at 1 and count up until you reach 3. Then, just take the square root of each number. Notice that √(1) = 1.
For cosine, just write everything backward. For tangent, just do the math that is tan(x) = sin(x) / cos(x).