Q&A for How to Remember the Trigonometric Table

Values of cosec, sec and cot can be found by taking inverse of sin, cos and tan respectively for the given angle.

The sine of 90° equals 1, and the cosine of 90° equals zero. It happens that the tangent of any angle is equal to its sine divided by its cosine. Thus, the tangent of 90° equals 1 divided by zero. However, dividing by zero is "undefined," because it equals infinity (which is not a defined number). That makes the tangent of 90° undefined.

You can reverse the numerator and denominator of sin to find cosec like (30°= 0= 1/0 i.e., not defined) and of cos to find sec.

Draw the polar triangle with the theta value and the two sides given by sin. They should be given to you in the form of a fraction, sin=opposite/hypotenuse. Then, use the Pythagorean theorem to solve for the third side and do cos=adjacent/hypotenuse.

It's a simple matter of memorization.

tan(x)=sin(x)/cos(x)

Graph the equations, sin(x), cos(x), tan(x), csc(x), sec(x), and cot(x). Use the x coordinates 0, 90, 180, 270, and 360 to see how each trigonometric function flows on the graph.

Calculate the ratio between the adjacent side and the hypotenuse, then look up that ratio in a cosine table, which will tell you the angle.

The author of this article chose not to display those functions. They're easily found, however: the secant of an angle is the reciprocal of its cosine, and the cosecant of an angle is the reciprocal of its sine.

Multiply both the numerator and the denominator by √2, i.e, (√2×√2)/(2 × √2) = 2/2√2 = 1/√2.

The number is greater than 180. So, anything that is greater than the sum on 180 times one.

The infinity symbol is used for undefined values.

The sine of any angle (in a right triangle) equals the side opposite the angle divided by the hypotenuse. In the case of a 90° angle, the opposite side is the hypotenuse, so the sine is the hypotenuse divided by itself, which is 1.

It's actually not undefined; tan(75) = 2 + √3. You can calculate it by dividing the sine of 75 by the cosine of 75.

Trigonometry has a lot of important applications in real life. It can be used to measure the heights of buildings and mountains, it's used in the development of video games, and even criminologists and archaeologists have to use trigonometry in their lines of work.

You have to learn the quadrant system of trigonometric ratios.

The maximum value of cosθ is 1, and the minimum value of cosθ is -1.

In the first row, put the values (0-4) in the formula (√x/2) i.e., √o/2, √1/2, √2/2, √3/2, √4/2 and you will get the entries for first row. For second row, just reverse the order of first row. In third row, use formula (tan (θ)= sin (θ)/cos (θ)), put values of sin and cos and you will get the answer. For the fourth row, use Cosec(θ)=1/sin(θ), for fifth, use sec(θ)=1/cos(θ). And for sixth, use cot(θ)= 1/tan(θ). That's it! You don't have to memorize.

There really is no proof, just a definition. 0! is defined as 1, which means that there is exactly one way to arrange the data set in 0! That arrangement is 0. Compare that with 3! = 6, where there are six ways to arrange the data set: 3 2 1, 3 1 2, 2 3 1, 2 1 3, 1 2 3, and 1 3 2. This is true of any factorial.

Cosecant and secant are the inverse of sine and cosine's numerator and denominator. 2 over the square root of 2 would be improper. Therefore, multiplying each by √2 would create 2√2/2. The 2s would cancel out leaving √2.

The best way to memorize trig identities is with a mnemonic device like SOHCAHTOA for calculating angles.

Secant and cosecant are the reciprocal values of cosine and sine. Inverse the numbers of whatever your cosine value is to find the secant. Inverse the numbers for your sine value to find the cosecant.

The cosecant is the ratio of the hypotenuse to the opposite side. (The opposite side is the denominator in the ratio.) When an angle is 0°, the opposite side has no length, so that the denominator in the ratio is zero. Dividing by zero is undefined.