When you see the table shown below of exact values of the trigonometric functions sin(x), cos(x) and tan(x) you always wonder "How am I going to remember them!?".
Here is an easy way to work them out without having to memorise them.
First of all the sine function increases from 0° to 90°.
sin(0°) = 0 and sin(90°) = 1
Step 1 Write the numbers 1, 2 and 3 from left to right in the empty cells in the sin(x) row as shown below.
Step 2 Square root these three numbers.
Step 3 Draw a fraction line underneath each number.
Step 4 Write a 2 at the denominator of each fraction.
... and this is how you can remember the exact values for the sine function from 0° to 90°.
The exact values for the cosine function from 0° to 90° can be worked out in a similar manner.
First of all the cosine function decreases from 0° to 90°.
cos(0°) = 1 and cos(90°) = 0
Step 1 Write the numbers 3, 2 and 1 from left to right in the empty cells in the cos(x) row as shown below.
Step 2 Square root these three numbers.
Step 3 Draw a fraction line underneath each number.
Step 4 Write a 2 at the denominator of each fraction.
... and this is how you can remember the exact values for the cosine function from 0° to 90°.