In summary: Beyond that, though, you need to be able to use "Half-Angle" and "Double-Angle" identities, recognize and manipulate "Cofunction" identities, and use the "Sum and Difference" identities. This is an easy-to-remember summary of the most basic concepts and techniques, which can be elaborated upon in the later grades, and are extremely useful in Calculus classes.In summary, trigonometric functions are often evaluated at special angles, which can be easily remembered using a unit circle and basic geometry principles. These special angles have degree measures of 30, 45, 60, 0, and 90, and their corresponding values for sine, cosine, and tangent can be derived using
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benorin
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In calculus classes when you are asked to evaluate a trig function at a specific angle, it’s 99.9% of the time at one of the so-called special angles we use in our chart. Since you are likely to have learned degrees first I’ll include degree angles in the first chart, but after that, it’s going to be radian only.
Begin by setting up the table on scratch paper as follows:
$$\begin{array}{ l| |c|c|c|c|c } \theta & 0 = 0º & \tfrac{\pi}{6} = 30º & \tfrac{\pi}{4}=45º & \tfrac{\pi}{3}=60º & \tfrac{\pi}{2}=90º \\ \hline\hline \sin\theta &   &   &  &   &    \\ \hline \cos\theta &   &    &    &    &    \\ \hline \tan\theta &    &    &    &   &    \\ \hline \end{array} $$
Then remember ##\sin\theta## starts at zero, fill in the pattern
$$\begin{array}{ l| |c|c|c|c|c } \theta & 0 & \tfrac{\pi}{6} & \tfrac{\pi}{4} & \tfrac{\pi}{3} & \tfrac{\pi}{2} \\ \hline\hline\sin\theta & \tfrac{\sqrt{0}}{2} & \tfrac{\sqrt{1}}{2} & \tfrac{\sqrt{2}}{2} & \tfrac{\sqrt{3}}{2} & \tfrac{\sqrt{4}}{2} \\...

Continue reading...
 
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I think I'll make this compulsory reading for my Maths students!
 
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In our junior classes, we learned it in a similar way:
##\theta~\rightarrow##​
0° = 0​
30° = ##\dfrac{\pi}{6}##​
45° = ##\dfrac{\pi}{4}##​
60° = ##\dfrac{\pi}{3}##​
90° = ##\dfrac{\pi}{2}##​
##\sin \theta##​
##\sqrt{\dfrac{0}{4}}##​
##\sqrt{\dfrac{1}{4}}##​
##\sqrt{\dfrac{2}{4}}##​
##\sqrt{\dfrac{3}{4}}##​
##\sqrt{\dfrac{4}{4}}##​
##\cos \theta##​
##\sqrt{\dfrac{4}{4}}##​
##\sqrt{\dfrac{3}{4}}##​
##\sqrt{\dfrac{2}{4}}##​
##\sqrt{\dfrac{1}{4}}##​
##\sqrt{\dfrac{0}{4}}##​
##\tan \theta##​
##\sqrt{\dfrac{0}{4 - 0}}##​
##\sqrt{\dfrac{1}{4 - 1}}##​
##\sqrt{\dfrac{2}{4 - 2}}##​
##\sqrt{\dfrac{3}{4 - 3}}##​
##\sqrt{\dfrac{4}{4 - 4}}##​
 
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"Trick"? The very basics of triangle Geometry and the Pythagorean Theorem, and The UNIT CIRCLE.

Easily enough done, drawing a Unit Circle and judging Sines and Cosines, and whichever other of the functions to derive what you need. Degree measures 30, 45, 60, 0, and 90, and 180 are the easy ones and are commonly used "Reference" angles.
 

Related to A Trick to Memorizing Trig Special Angle Values Table

1. How do I use the "A Trick to Memorizing Trig Special Angle Values Table"?

The trick involves using a mnemonic device to remember the values of the sine, cosine, and tangent of special angles (0°, 30°, 45°, 60°, and 90°). It is a helpful tool for quickly calculating these values without having to use a calculator.

2. What is the mnemonic device used in the trick?

The mnemonic device is "SOH-CAH-TOA", which stands for "Sine equals Opposite over Hypotenuse", "Cosine equals Adjacent over Hypotenuse", and "Tangent equals Opposite over Adjacent".

3. Why is it important to memorize these special angle values?

Knowing the values of these special angles can be useful in various fields, such as mathematics, engineering, and physics. It can also save time when solving trigonometric equations or problems.

4. How can I practice and reinforce my memorization of the special angle values?

One way to practice is by using flashcards or creating a study guide with the values and their corresponding angles. You can also try solving different types of problems that involve these special angles.

5. Are there any other tips for memorizing the trig special angle values table?

Aside from using the mnemonic device, you can also try creating visual aids, such as diagrams or charts, to help you remember the values. It may also be helpful to understand the relationship between the special angles and the unit circle.

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