45 degrees in radians is π/4. (The full circumference is 2πr, 180 degrees is π and 45 degrees is π/4) sin π/4 = cos π/4 because the two sides are equal. tan π/4 = tan 45 = 1. Arctan(1) is the degree (or radian) which returns a value of 1. So arctan of 1 …

2016年8月28日 · In figuring the argument for $3 + 4i$ you want the angle so that $\tan x = 4/3$. This is $\arctan 4/3$ or $\tan^{-1} 4/3$. Obviously you do not figure this out by making a fraction out of $\frac 1{\tan 4/3}$. You were right to be confused--- that wouldn't make any freaking sense. So ... you are probably asking how do you calculate $\arctan 4/3 ...

2016年4月2日 · With these three cases established, we can now look at the identity: $$\tan(\alpha+\beta)=\frac{\tan(\alpha)+\tan(\beta)}{1-\tan(\alpha)\tan(\beta)}$$

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2017年4月21日 · Converting to radians gives $\mathrm{arctan}(1)=\pi/4$. Finding the exact arctangent of other values would be much more complicated, though you ought to be able to estimate the arctangent by picturing it. For example, it's easy to estimate that $\mathrm{arctan}(1/3)$ should be about $15$ or $20$ degrees, just by picturing a …

2016年12月27日 · As we want $\arctan$ to be a function, we have to choose a range of output values. When you use the $\arctan$ to get the polar angle, there is an uncertainty of $\pi$ because $\tan (x+\pi)=\tan x$. You have to use the real and imaginary parts to decide the multiple of $\pi$ to add to the $\arctan$ output to get the proper polar angle you want.

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2019年1月15日 · Adding angles corresponds to multiplying complex numbers. $\arctan(\theta)$ is the angle (argument) of the complex number $1+\theta i.$ Then

It only equals $\theta $ if $$-\frac {\pi}{2}<\theta < \frac {\pi}{2} $$ as the range of $\arctan$ is only from $-\frac {\pi}{2} $ to $\frac {\pi}{2} $. If $\theta $ is outside this interval, then you would need to add or subtract $\pi $ from $\theta $ until you get to the angle in …

2017年12月4日 · $$\arctan 1=\dfrac{\pi}{4}$$ Remark 1 : A domain of validity of formula (1) is for angles $\alpha, \beta, \gamma \in (0, \pi/2)$ such that $\alpha+\beta+\gamma \in (0, \pi/2)$ as well. Here, these conditions are fulfilled.