Omar – (2)I am worried about tomorrow’s Maths test.
(3)Even after trying for several times to memorize the table of trigonometric ratios,
I fail to recollect it.
Victor – (4)Don’t worry Omar. (5)I know an easy technique to remember the trigonometric
ratios.
(6)Look at your left hand.
The thumb denotes 0°, the index finger denotes 30°, the middle finger denotes 45°, the
ring finger denotes 60° and the little finger denotes 90°.
Let us find out the values of sin and cos.
We later calculate other trigonometric values.
(7)In this method, depending on whether it is sine or cosine, count the number of fingers
towards left or right respectively.
(8)Then divide the number by 4 and take the square root of this ratio.
(11)For sin 0°, count the number of fingers to the left of the thumb.
(12)It’s 0.
0 divided by 4 is 0.
(12-A)The square root of 0 is 0.
Hence, sin 0° is 0.
(12-B)For cos 0°, count the number of fingers to the right of the thumb.
It’s 4.
4 divided by 4 is 1.
The square root of 1 is 1.
Hence, cos 0° is 1.
(13)For sin 30°, count the number of fingers to the left of the index finger.
It’s 1.
1 divided by 4 is 1/4.
The square root of 1/4 is 1/2.
Hence, sin 30° is 1/2.
(14)For cos 30°, count the number of fingers to the right of the index finger.
It’s 3.
3 divided by 4 is 3/4.
The square root of 3/4 is √3/2.
Hence, cos 30° is √3/2.
(15)For sin 45°, count the number of fingers to the left of the middle finger.
It’s 2.
2 divided by 4 is 1/2.
The square root of 1/2 is 1/√2.
Hence, sin 45° is 1/√2.
(16)For cos 45°, count the number of fingers to the right of the middle finger.
It’s 2.
2 divided by 4 is 1/2.
The square root of 1/2 is 1/√2.
Hence, cos 45° is 1/√2.
(17)For sin 60°, count the number of fingers to the left of the ring finger.
It’s 3.
3 divided by 4 is 3/4.
The square root of 3/4 is √3/2.
Hence, sin 60° is √3/2.
(24)For cos 60°, count the number of fingers to the right of the ring finger.
It’s 1.
1 divided by 4 is 1/4.
The square root of 1/4 is 1/2.
Hence, cos 60° is 1/2.
(25)For sin 90°, count the number of fingers to the left of the little finger.
It’s 4.
4 divided by 4 is 1.
The square root of 1 is 1.
Hence, sin 90° is 1.
(26)For cos 90°, count the number of fingers to the right of the little finger.
It’s 0.
0 divided by 4 is 0.
The square root of 0 is 0.
Hence, cos 90° is 0.
(27)Now that you know the values for sin Θ and cos Θ, you can find the other values.
(28)We can find out the cosec Θ by taking the reciprocal of sin Θ.
(29)sec Θ can be found out by taking the reciprocal of cos Θ.
(30)tan Θ can be found out by taking the ratio of sin Θ and cos Θ.
(31)cot Θ can be found out by taking the reciprocal of tan Θ.
(32)So Omar, wasn’t this easy?
(34)Omar – Now after learning this trick, I can actually build up the entire trigonometric
table at my fingertips.