Trigonometry?

Question

What's a good way to memorize the trigonometric values of common angles? I have to know them by Friday.

Answer 1

If you mean that you want to remember the values of the trig functions of various common angles, the easiest way to do it is to remember the common triangles that have those angle in them.

For 45 degrees, remember the right triangle with its two sides each one unit long. The hypotenuse, then has to be equal to the square root of 2 (Pythagorean Theorem). So the sin and cos of 45 is 1/root 2.

For 30 and 60 degrees, the triangle is a 30 - 60 - 90 right triangle. If the short side of this triangle (which is opposite the 30 degree angle) is 1 unit, and the hypotenuse is 2, then the other side is sqrt 3. So you can remember sin and cos of 30 and 60 by remembering which side goes over the hypotenuse.

You can obviously figure out the tangents, cotangents, secant, cosecant just as easily.

Answer 2

I would remember the ratio of the sides of 30-60-90 and 45-45-90 triangles and the trigonometric function definitions. No need to memorize what you can figure out.

Answer 3

The above answers are all very good.

I prefer, however, to memorize the values of each of the important angles from 0-90 degrees, and then extending them around the whole 360 degree circle.

Draw a set of axis, and then draw a circle with a radius of 1 unit, centered around (0,0)

Think of 0 degrees as a line from (0,0) to (1,0), 90 degrees as a line from (0,0) to (0,1), 180 degrees as a lone from (0,0) to (-1,0), 270 degrees as a line from (0,0) to (0,-1), and 360 degrees is your same line at 0 degrees.

Now, consider your Cosine value to be the x-value of your new lines. Your Sine value is the y-value of your lines.

Memorize these:
0 degrees - (1,0) - [cosine = 1, sine = 0]
30 degrees - (sqrt(3) / 2, 1/2) - [cosine = sqrt(3) / 2, sine = 1/2]
45 degrees - (sqrt(2) / 2, sqrt(2) / 2) - [cosine = sqrt(2) / 2, sine = sqrt(2) / 2]
60 degrees - (1/2, sqrt(3) / 2) - [cosine = 1/2, sine = sqrt(3) / 2]
90 degrees - (0,1) - [cosine = 0, sine = 1]

With those memorized, you can figure the cosine or sine for any value from 0-360 in multiples of 15. Just run along farther on your circle, and adjust for any Negatives, depending on the quadrant.

At first, draw this circle out on the side of your paper. When you get good, you can picture the circle in your head and do the calculation quickly, and when you get really good, these numbers will just come to you instantly.

Answer 4

there's no need to memorize the trigonometric table just bring it with you on friday.

Answer 5

You need to know and be familar with
30-60-90 special triangle: hyp = 2*short leg, long leg = √3 * short leg
45-45-90 special triangle: hyp = √2 * leg

Answer 6

nicely it relies upon on the main important you're doing in college, or the faculty you're attending i'm analyzing pharmaceutical technology, and it does require me to take Calculus, which does contain slightly of trig. different than that, no longer possibly, until eventually you desire to calculate the value of what number miles in keeping with hour you're using on a speedway. ahaha