When is $\\sin(x) = \\cos(x)$? - Mathematics Stack Exchange
2016年8月28日 · 1) cos2 x +sin2 x = 1. So 2cos2 x = 1. So cos x = sin x = ± 12−−√. 2) sin x is the adjacent side of a right triangle. cos x is the opposite side. sin x = cos x means the triangle is isoceles. So the base angles are congruent. So x + x + 90 = 180. 3) sin x = cos(π 2 − x) so cos x = sin x = cos(π 2 − x)
What is $\sin (\cos (x))$? - Mathematics Stack Exchange
2015年11月26日 · As the title asks, what is $\sin(\cos(x))$. I want it to be reduced more, if possible. I don't know where to start. I could manipulate the expression in many ways, but none allow me to remove either the $\sin$ or $\cos$. For example:$$\sin(\cos(x))=\sqrt{1-(\cos(\cos(x))^2}$$ Then I'd need to know what $\cos(\cos(x))$ is.
trigonometry - How can we sum up $\sin$ and $\cos$ series when …
$\begingroup$ @onepound: The big right triangle (with "trigonography.com" along its hypotenuse) has a hypotenuse length of $\sin n\theta/\sin\theta$.
Why use sine and cosine when resolving vectors into components?
2017年5月7日 · The vector is the diagonal of a unique rectangle. The horizontal and vertical components of the vector are by definition the horizontal and vertical sides of the rectangle; that's just the statement that moving from the origin to the endpoint along the ray gives the same ending location as moving only horizontally and then only vertically along those sides.
trigonometry - when to use sine vs cosine vs tangent
2014年2月14日 · If $\tan x$ is known, then $\cos x=\dfrac1{\sqrt{1+\tan^2x}}$ and $\sin x=\dfrac{\tan x}{\sqrt{1+\tan^2x}}$ . Basically, given Pythagoras' theorem , if we know the ratio between any two sides, the other two ratios soon follow.
trigonometry - Why $\sin(n\pi) = 0$ and $\cos(n\pi)=(-1)^n ...
1. If you go through the unit circle process, then you see how they are equivalent. But if you want a proof then: You may observe the fact that sin(0) = 0. Then you may prove that sin(x + π) = sin(x) and sin(x − π) = sin(x) using angle addition formulas. Having done this you prove: sin(0 ± …
Easy way of memorizing values of sine, cosine, and tangent
2015年12月1日 · 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. Step 7: You can extend the table for further angles by using formulas such as
trigonometry - How to simplify $\sin^4 x+\cos^4 x$ using ...
$\sin^{4}x+\cos^{4}x$ I should rewrite this expression into a new form to plot the function. \begin{align} &; = (\sin^2x)(\sin^2x) - (\cos^2x)(\cos^2x) \\ & ...
Proof of the identity $\\sin(x+y) =\\sin(x)\\cos(y) + \\cos(x)\\sin(y ...
2017年8月6日 · This requires that the two matrices must be equal, so $\sin(a+b) = \cos a \sin b + \sin a \cos b$ (and also, $\cos(a+b) = \cos a \cos b - \sin a \sin b$!). Share Cite
trigonometry - Where do trigonometric functions belong in the …
2020年8月30日 · The result of a function is a number, and that's what we treat it as, a number (and so if we need to evaluate the expression, we're going to have to evaluate the function before we can perform the rest of the operations. e.g. we can't do sin(x)+2 if we don't know what sin(x) is yet). $\endgroup$