trigonometry table

remember the above values:

(a) divide the numbers 0, 1, 2, 3 and 4 by 4,

(b) take the positive square roots,

(c) these numbers given the values of sin 0°, sin 30°, sin 45°, sin 60° and sin 90° respectively.

(d) write the values of sin 0°, sin 30°, sin 45°, sin 60° and sin 90° in reverse order and get the values of cos 0°, cos 30°, cos 45°, cos 60° and cos 90° respectively.

If θ be an acute angle, the values of sin θ and cos θ lies between 0 and 1 (both inclusive).

The sine of the standard angles 0°, 30°, 45°, 60° and 90° are respectively the positive square roots of 0/4,1/4, 2/4,3/4 and 4/4  

Therefore,

sin 0° = √(0/4) = 0

sin 30° = √(1/4) = ½

sin 45° = √(2/4) = 1/√2 = √2/2

sin 60° = √3/4 = √3/2;

cos 90° = √(4/4) = 1.

Similarly  cosine of the above standard angels are respectively the positive square roots of 4/4, 3/4, 2/4, 1/4, 0/4

Therefore,

cos 0° = √(4/4) = 1

cos 30° = √(3/4) = √3/2

cos 45° = 1

cos 60° = √(1/4) = 1/2

cos 90° = √(0/4) = 0.

Since, we know the sin and cos value of the standard angles from the trigonometrical ratios table; therefore we can easily find the values of the other trigonometrical ratios of the standard angles.

The tangent of the standard angles 0°, 30°, 45°, 60° and 90°:

tan 0° = 0

tan 30° = √3/3

tan 45° = √(2/4) = 1/√2 = √2/2

tan 60° = √3

tan 90° = not defined.

The cosine of the standard angles 0°, 30°, 45°, 60° and 90°:

csc 0° = not defined.

csc 30° = 2

csc 45° = √2

csc 60° = 2√3/3

csc 90° = 1.

The secant of the standard angles 0°, 30°, 45°, 60° and 90°:

sec 0° = 1

sec 30° = 2√3/3

sec 45° = √2

sec 60° = 2

sec 90° = not defined.

The cotangent of the standard angles 0°, 30°, 45°, 60° and 90°:

cot 0° = not defined.

cot 30° = √3

cot 45° = 1

cot 60° = √3/3

cot 90° = 0