Trigonometric table helps you to understand and grasp values of trigonometric ratios in an efficient manner. It is a simple collection of values of trigonometric ratios for various standard angles. The trigonometric table comprises six ratios for various degrees such as 30°, 60°, 90°, etc. The table seems to be tough to learn at the very first time but is very easy to understand. The values of trigonometric ratios are very important to solve various trigonometric problems. Let us see how the trigonometric table looks like.
|
Radians |
Degrees |
Sin θ |
Cos θ |
Tan θ |
Cosec θ |
Sec θ |
Cot θ |
|
0 |
0° |
0 |
1 |
0 |
Not defined |
1 |
Not defined |
|
Ï€/6
|
30° |
1/2 |
|
3 |
2 |
2 |
|
|
Ï€/4
|
45° |
|
|
1 |
|
|
1 |
|
Ï€/3 |
60° |
|
1/2 |
|
2 |
2 |
|
|
Ï€/2 |
90° |
1 |
0 |
Not defined |
1 |
Not defined |
0 |
Trigonometric Ratios
The ratio of the length of sides of a triangle is known as trigonometric ratio. These ratios in the trigonometric table relate to the ratios of sides of a right triangle to the respective angle. Isn’t it easy to understand? No! Let us try a different way out. The basic trigonometric ratios are sine, cosine, and tangent. Other than these mentioned trigonometric ratios, there are three other ratios namely cosecant, secant, and cotangent. These ratios are derived from sine, cosine, and tangent respectively. Let us try to understand the trigonometric ratios in detail.
Using the measure of acute angle, we can calculate the values of these trigonometric ratios, where 'p' is the perpendicular, 'b’ is the base and 'h' is the hypotenuse. Let there be a right-angled triangle ABC. Then, the following can be defined as the six trigonometric ratios:
●Sine: For any given angle, the ratio of the perpendicular to the hypotenuse is defined as the sine ratio. In each right-angled triangle, the sine ratio can be given as, AB/AC that is Perpendicular/Hypotenuse.
● Cos: For any given angle, the ratio of the base to the hypotenuse is defined as the cosine ratio. In each right-angled triangle, the cosine ratio can be given as, BC/AC that is Base/Hypotenuse.
● Tangent: For any given angle, the ratio of the perpendicular to the base is defined as the tangent ratio. In each right-angled triangle, the tangent ratio can be given as AB/BC that is Perpendicular/Base.
● Cosecant: For any given angle, the ratio of the hypotenuse to the perpendicular is defined as the cosecant ratio. In each right-angled triangle, the cosecant ratio can be given as AC/AB that is Hypotenuse/Perpendicular.
● Secant: For any given angle, the ratio of the hypotenuse to the base is defined as secant ratio. In each right- angled triangle the secant can be given as AC/BC that is Hypotenuse/Base.
●Cotangent: For any given angle, the ratio of the base to the perpendicular is defined as cotangent ratio. In each right-angled triangle the cotangent can be given as BC/AB that is Base/Perpendicular.
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A Simple Trick to Recall Trigonometric Ratios
These ratios can be easily learned by using a simple method. Here we can use an acronym that is “Pandit Badri Prasad Har Har Bole”, where the letter ‘P’ in the front signifies perpendicular, ‘B’ signifies base, and ‘H’ signifies hypotenuse respectively. Now if we divide Pandit by Har it signifies, Perpendicular/Hypotenuse which is the formula of sine ratio. Similarly, cosine ratio and tangent ratio can be calculated by using this trick. For the other three ratios namely, cosecant, secant, and cotangent, simply reverse the values of sine, cosine, and tangent respectively to get the values of cosecant, secant, and cotangent. If you want to learn more about these concepts in detail and in an interactive and a fun way with the best tutors, visit Cuemath.
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