Content

• To step
• Tips
• Warnings

Have you ever had trouble remembering the sine or tangent of angle? This article explains how to easily learn basic trigonometric numbers for the most common angles.

To step

1. Create a table. In the first row you write down the trigonometric ratios (sin, cos, tan, cot). In the first column you write down the angles (0 °, 30 °, 45 °, 60 °, 90 °). Leave the rest of the boxes empty.
2. Fill in the sine column. We fill in the empty boxes of the sine column with the equation √x / 2. When the sine column is filled, we can fill in the rest of the columns effortlessly!
   • For the 1 value in the sine column (so, sin 0 °); set x = 0 and use this in the equation √x / 2. So, sin 0 ° = √0 / 2 = 0/2 = 0
   • For the 2 value in the sine column (so, sin 30 °); set x = 1 and use this in the equation √x / 2. So, sin 30 ° = √1 / 2 = 1/2
   • For the 3 value in the sine column (so, sin 45 °); set x = 2 and use this in the equation √x / 2. So, sin 45 ° = √2 / 2 = 1 / √2
   • For the 4 value in the sine column (so, sin 60 °); set x = 3 and use this in the equation √x / 2. So, sin 60 ° = √3 / 2.
   • For the 5 value in the sine column (so, sin 90 °); set x = 4 and use this in the equation √x / 2. So, sin 90 ° = √4 / 2 = 2/2 = 1.
3. Fill the cosine column. Just copy the values ​​from the sine column in reverse order into the cosine column. This is possible because sin x ° = cos (90-x) ° for each x.
4. Fill in the tangent column. We know that tan = sin / cos. So for each angle, you take the sine and divide it by the value of cosine for the corresponding value of tangent. For example, tan 30 ° = sin 30 ° / cos 30 ° = (√1 / 2) / (√3 / 2) = 1 / √3
5. Fill the cotangent column. Just copy the values ​​from the tangent column in reverse order into the cotangent column. This is possible because tan x ° = sin x ° / cos x ° = cos (90-x) ° / sin (90-x) ° = cot (90-x) ° for each x.

Tips

• Do not leave irrational numbers in the denominator. For example, tan30 ° = 1 / √3. Don't leave it like that, but rewrite it as √3 / 3.

Warnings

• Dividing by 0 is not possible! tan90 ° = ± ∞ and cot0 ° = ± ∞, but ∞ is not considered an actual number, so do not write it that way. Instead, write this as "undefined" or "n / a" (invalid).