How were the sine, cosine and tangent tables originally calculated?
Sine, cosine, tangent: defined as ratios in a right triangle, but how to understand the negative values for angles outside 0-90 degrees? 0 Why, in physics, isn't the law of sine used as often as the law of cosine?
Easy way of memorizing values of sine, cosine, and tangent
2015年12月1日 · You end up with the values of sine 0,30,45,60 and 90. Drawing Sin Cos Tan Table. Step 5(orange):Once you have values for sine function, invert them for cosine i.e( sin 90 = cos 0, sin 60 = cos 30, sin 45 = cos 45 and so on) and you get values for cosine function. Step 6: For tangent, put sin/cos values and simplify.
Why use sine and cosine when resolving vectors into components?
2017年5月7日 · I have always wondered why you have to use sine and cosine instead of a proportional relationship, such as $(90-\text{angle})/90$. I cannot seem to find an answer anywhere online. Using my linear relationship, when the angle is $0$, then $90/90$ is $1$ and the component is at its maximum value, and when the angle is $90$, the component is $0 ...
How many ways are there to define sine and cosine?
2015年7月27日 · Unit circle definition: the sine (cosine) of a directed angle with vertex at the origin and initial ray on the positive x-axis is the y-coordinate (x-coordinate) of the point of intersection of the terminal ray of the angle with the unit circle centered at the origin.
calculus - Orthogonality of sine and cosine integrals.
Orthogonality lemma sine and cosine. 1. Limit of Cosine and Sine Fourier Transforms. 0.
trigonometry - when to use sine vs cosine vs tangent
2014年2月14日 · If you know the sides you can work out the angles. If you know the angle you can work out the length of the sides. Is this a correct assumption? So, is it correct so assume that if you know one of the angles besides the 90 degree angle and 1 length of one side you can determine the sine, cosine and tangent of that triangle?
How to calculate the sine manually, without any rules, calculator or ...
2018年7月16日 · They created tables of sine values (actually chord values, in really ancient times, but that more or less amounts to the same problem) by starting with $\sin(0^\circ)=0$, $\sin(90^\circ)=1$ and then using known formulas for $\sin(v/2)$ to find sines of progressively smaller angles than $90^\circ$, and then formulas for $\sin(v+u)$ to find sines ...
Is there a way to get trig functions without a calculator?
The formulae for sine and cosine are the ones to focus on first. They converge very quickly, but you have to realise that the angles are measured in radians, where $2\pi$ radians $=360^{\circ}$. If you do the conversion, you'll be able to calculate quite quickly for yourself.
How can we sum up $\\sin$ and $\\cos$ series when the angles …
Likewise for the sine function identity, follow the same procedure and take the imaginary part of the sum ...
How can I understand and prove the "sum and difference …
Cosine, Cosine, Co-Sign, Sine, Sine! The first line encapsulates the sine formulas; the second, cosine. Just drop the angles in (in order $\alpha$ , $\beta$ , $\alpha$ , $\beta$ in each line), and know that "Sign" means to use the same sign as in the compound argument ("+" for angle sum, "-" for angle difference), while "Co-Sign" means to use ...