May i ask what are the values of sin cos and tan, also sin-1 cos-1 and tan-1
If somebody wanted to make a trigonamatry "calculator" where you enter your values and it does all the working out for you, what would the variable sin cos tan be? (also sin-1 cos-1 tan-1)
I do not understand your question. What do you mean, "what are the values of sin cos and tan, also sin-1 cos-1 and tan-1?"
Trig functions don't have "values" like constants (such as Pi and e). Sin(pi) will equal 0, but so will Sin(kPi), with k being an integer. Sine and Cosine are both ratios, with Tangent being equal to Sin/Cos.
As far as arctan, arcsin, and arccos (arccos is the same as cos-1), that's simply the inverse, replace x and y. For instance, the value of arccos(1) will be 0 because cos(0)=1. Does that help any? I'm terrible at teaching and even worse at doing it online in text.
Alternatively
e^ix=Cos(x) + iSin(x)
so Cos is the real part of e^ix and Sin is the imaginary part of e^ix
I once tried to think of a simple way to explain the trig functions without using ideas from higher math. First of all, you need to know that they are not simply a single value. For every angle, there is a unique number between -1 and 1 which is its sine. Sine is the actual name of the function, but mathematicians like to shorten it to sin so they can write something like sin(45 degrees) = .707 or sin(90 degrees) = 1.
Consider the sine function to be the "closing door" function. When the door is fully open ( 0 degrees ) the apparent width of the door is zero, since you view it edge-on. When the door is half closed ( 45 degrees ) you might think the apparent width of the door would be 1/2 the full width, but if you try it you will see that it's a bit more than that, in fact slightly more than 7/10 the full width of the door, When the door is fully closed, you see the full width of the door. So we have sin(0) = 0, sin(45) = .707, and sin(90) = 1. I can explain how the cosiine (or cos) is the "opening door" function, starting at 1, if you haven't gone to sleep yet. Sin-1 of course means "the angle whose sin is" whatever number is plugged into the function.
Great Ideas! I love reading this post. Sin cos tan I love mathematics.
(((-1)^n)x^(2n+1))/(2n+1)!
