I've been told that
sin(c+h)=sin(c)xcos(h)+cos(c)xsin(h)
but how?
please explain
Here you will find a proof of that trigonometric identity:
http://library.thinkquest.org/C0110248/trigonometry/formsine.htm
Here is another approach to the proof
http://www.themathpage.com/aTrig/sum-proof.htm
(there seems to be a 'spacing' problem in the html code in the first few lines, but I am sure you know what the equation should read )
The formula you mentioned is known as the sum of angles formula for sine. To explain how it works, let's break it down step by step:
1. Start with the expression sin(c+h). This represents the sine of the sum of two angles, c and h.
2. Next, we utilize the angle addition formula for sine, which states that sin(a+b) = sin(a)cos(b) + cos(a)sin(b). We substitute a with c and b with h, giving us: sin(c+h) = sin(c)cos(h) + cos(c)sin(h).
3. The formula derives its validity from the trigonometric properties of sine and cosine functions. Specifically, sin(x) represents the y-coordinate of a point on the unit circle, and cos(x) represents the x-coordinate. By applying these properties, we can prove the formula to be true.
So, in summary, the formula sin(c+h) = sin(c)cos(h) + cos(c)sin(h) is a result of the angle addition formula for sine, which is derived from the properties of the sine and cosine functions.