9th Grade Math > Trigonometric Ratios > Easily Memorizing the Values of Sine, Cosine, and Tangent for 30°, 45°, and 60° Angles, Practice Worksheets

 Many students try to memorize the trigonometric values for the special angles 30°, 45°, and 60° by rote, but there is an easier way. The trigonometric values follow a pattern, making them easier to remember than you might think.

Let's start with a table of the trigonometric ratios for these special angles.

30°:

• sin: 1/2
• cos: √3/2
• tan: 1/√3

45°:

• sin: √2/2
• cos: √2/2
• tan: 1

60°:

• sin: √3/2
• cos: 1/2
• tan: √3

First, notice the pattern for sin 30°, sin 45°, and sin 60°: the denominators are all 2, and the numerators increase by √1, √2, and √3.

Next, for cosine, the values follow the same pattern but in reverse order.

Additionally, these values are symmetric around 45°.

Finally, the tangent values follow a simple pattern where the value of tan 30° is multiplied by √3.

This makes memorizing the sine, cosine, and tangent values for 30°, 45°, and 60° much easier. Having these values memorized is essential, but using these patterns can help lighten the load and boost your confidence in math.

To further practice these values, you can generate and print problems from the 'Modoo Math' site. Below is an example problem created by Modoo Math.