The representation of the trigonometric function angle value is the trigonometric function table.  We have 3 major trigonometric functions Sine, Cosine, Tangent and 3 minor trigonometric functions Cosecant, Secant, Cotangent. 

The table typically includes degrees and radians along with the corresponding angle value. The commonly used values are 0,30,45,60,90 degrees. 

Trigonometric function table have various applications. Using this table we can solve the trigonometric function problem and we can find the unknown angles. 

Memorizing the trigonometric function values for common angles (0°, 30°, 45°, 60°, 90°) can be made easier with a few simple tricks. Here’s a step-by-step method:

1. Remember the Angle Order: 

The common angles are: 0°, 30°, 45°, 60°, 90°

2. Sine Function (sin θ):

Write the angles in order: 0°, 30°, 45°, 60°, 90°

For sin θ, take the square roots of 0, 1, 2, 3, 4 and divide by 2:

\sin\theta = \frac{\sqrt{0}}{2}, \frac{\sqrt{1}}{2}, \frac{\sqrt{2}}{2}, \frac{\sqrt{3}}{2}, \frac{\sqrt{4}}{2}

simplified 

\sin 0\degree = 0,\quad\sin 30\degree = \frac{1}{2},\quad \sin 45\degree = \frac{\sqrt{2}}{2},\quad\sin 60\degree = \frac{\sqrt{3}}{2},\quad \sin 90\degree = 1,

3. Cosine Function (cos θ):

Cosine is the reverse of sine for these angles:

\sin\theta = \frac{\sqrt{4}}{2}, \frac{\sqrt{3}}{2}, \frac{\sqrt{2}}{2}, \frac{\sqrt{1}}{2}, \frac{\sqrt{0}}{2}

simplified 

\cos 0\degree = 1,\quad \cos 30\degree = \frac{\sqrt{3}}{2},\quad \cos 45\degree = \frac{\sqrt{2}}{2},\quad \cos 60\degree = \frac{1}{2},\quad \cos 90\degree = 0,

4. Tangent Values (tan θ):

\tan \theta = \frac{\sin \theta}{\cos \theta}:

\tan 0^\circ = 0, \quad \tan 30^\circ = \frac{1}{\sqrt{3}}, \quad \tan 45^\circ = 1, \quad \tan 60^\circ = \sqrt{3}, \quad \tan 90^\circ = \text{undefined},

Hand Trick (Optional):
Use your left hand (palm facing you) to represent angles:

0° (thumb), 30° (index), 45° (middle), 60° (ring), 90° (pinky).

For sin θ, count fingers below the angle finger, take the square root, and divide by 2.

For cos θ, count fingers above the angle finger, take the square root, and divide by 2.

Practice:
Write the table 2-3 times while saying the values aloud.

Quiz yourself by covering one column and recalling it.