Prove that $\arccos x + \arccos(-x) = \pi$ when $x \in [-1,1]$. How do I prove this? Where should I begin and what should I consider?

In mathematics, the inverse trigonometric functions (occasionally also called antitrigonometric, [1] cyclometric, [2] or arcus functions [3]) are the inverse functions of the trigonometric functions, under suitably restricted domains.

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Mar 20, 2015 · Let ##\alpha=\cos^{-1}(-x)## and ##\beta = \cos^{-1}x##. To show ##\alpha = \pi -\beta##. ##\alpha## and ##\pi - \beta## are both in ##[0,\pi]##, so if their cosines are equal, the angles are equal. ##\cos\alpha = -x## ##cos(\pi - \beta) = \cos\pi\cos\beta+\sin\pi\sin\beta = -\cos\beta = -x##

Online arccos (x) calculator. Inverse cosine calculator. Enter the cosine value, select degrees (°) or radians (rad) and press the = button.

What is the general solution for arccos (x)= pi/3 ?

Hint: $\arccos\left(2x\right)=\arccos\left(x\right)+\pi/3$. Now take the cosinus on both sides and see what happens.

Jan 24, 2015 · By definition, $\arcsin(x)$ is the angle $\alpha$ such that $\sin(\alpha) = x$ and $-\pi/2 \le \alpha \le \pi/2$, while $\arccos(x)$ is the angle $\beta$ such that $\cos(\beta) = x$ and $0 \le \beta \le \pi$.

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Take the inverse arccosine of both sides of the equation to extract x x from inside the arccosine. Simplify the right side. Tap for more steps... The result can be shown in multiple forms. Exact Form: Decimal Form: