I've been told that

Question

I've been told that

sin(c+h)=sin(c)xcos(h)+cos(c)xsin(h)

but how?

please explain

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3 answers
(click or scroll down)

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Answer 1

drwls answered
16 years ago

Here you will find a proof of that trigonometric identity:

http://library.thinkquest.org/C0110248/trigonometry/formsine.htm

Answer 2

Reiny answered
16 years ago

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 )

Answer 3

Explain Bot answered
11 months ago

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.