Sin Table – Trigonometry Table – Values – Examples

Sin Table

In a right-angled triangle, sine of any acute angle is equal to the ratio of the opposite side to the hypotenuse.

\operatorname{Sin} \theta=\frac{\text { Side opposite to } \theta}{\text { Hypotenuse }}

Angles are measured in degrees or radians. To convert degrees into radians, multiply \left(\frac{\pi}{180^{\circ}}\right)with the given degree.

There are some standard angles that are frequently used for calculations and the sin values of these angles should be remembered. These standard angles are 0°, 30°, 45°, 60° and 90°.

Sin table is the part of the trigonometry table. It shows the values for sine of standard angles. 

Sin Table for standard angles

Trick to remember the above table

1. Write the standard angles in ascending order.

2. Under these angles write 0 to 4 from left to right and divide them by 4.

3. Take the square roots of the numbers shown in step 2.

4. Compile the table in step 1 and step 3.

Formulas used in calculations

Given below are some basic formulas used in solving problems related to trigonometry.

Complementary angles formula

1. \sin x=\cos \left(90^{\circ}-x\right)
2. \cos x=\sin \left(90^{\circ}-x\right)
3. \tan x=\cot \left(90^{\circ}-x\right)
4. \cot x=\tan \left(90^{\circ}-x\right)
5. \sec x=\operatorname{cosec}\left(90^{\circ}-x\right)
6. \operatorname{cosec} x=\sec \left(90^{\circ}-x\right)

Reciprocal Formulas

\text { 1. } 1 / \sin x=\operatorname{cosec} x

2.  1/ \cos x=\sec x
3.  1/ \tan x=\cot x

We have also given the sine values from 0 degrees to 90 degrees for your reference.

Sin chart (0° to 90°)

Solved Examples

1. What is the value of cos 45°?

cos 45° = sin (90° – 45°) 

              = sin 45°

= \frac{1}{\sqrt{2}}

2. Find the value of cot 30°.

Sin 30° = ½

Cos 30° = sin (90° – 30°) 

               = sin 60° 

= \frac{\sqrt{3}}{2}

\cot 30^{\circ}=\frac{\cos 30^{\circ}}{\sin 30^{\circ}}=\frac{\sqrt{3} / 2}{1 / 2}=\sqrt{3}

Hence the value of cot 30° is equal to\sqrt{3}

3. Calculate the value of (cos 45° – sin 30°).

\cos 45^{\circ}=\frac{1}{\sqrt{2}}
\sin 30^{\circ}=\frac{1}{2}
\cos 45^{\circ}-\sin 30^{\circ}=\frac{1}{\sqrt{2}}-\frac{1}{2}=\frac{\sqrt{2}-1}{2}
Hence the value of \left(\cos 45^{\circ}-\sin 30^{\circ}\right) is equal to \frac{\sqrt{2}-1}{2}