Graph of arccos x (inverse cosine)

Updated 20 October 2026 · Values computed by the ihateDesmos engine

The inverse cosine graph falls from (−1, π) to (1, 0), passing through (0, π/2). It is the cosine curve on 0 ≤ x ≤ π, reflected in the line y = x.

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The graph of

y=arccos(x)

for −3 ≤ x ≤ 3. Dots mark its root and y-intercept.

Key features

Domain: −1 ≤ x ≤ 1
Range: 0 ≤ y ≤ π
End points: (−1, π) and (1, 0)
Monotonic: Decreasing on its whole domain
Vertical tangents: At x = ±1
Symmetry: arccos(−x) = π − arccos x: symmetric about the point (0, π/2)
y-intercept: (0, 1.5708)
Derivative: −1√1−x²
Antiderivative: xarccos(x)−√1−x²+C

Derivative and antiderivative from the calculator’s algebra system. Domain, range and asymptotes are stated for real x.

What the graph of arccos x looks like

Cosine is restricted to 0 ≤ x ≤ π, where it falls from 1 to −1 exactly once, and arccos inverts that piece. The result is a decreasing curve from (−1, π) down to (1, 0).

It is neither odd nor even, but it has point symmetry about (0, π/2): arccos(−x) = π − arccos x. In fact arccos x = π/2 − arcsin x, so the arccos graph is the arcsin graph reflected in the x-axis and lifted by π/2.

Like arcsin, the curve is vertical at its end points, where the derivative −1/√(1 − x²) becomes infinite.

Points of interest

Found numerically to about twelve digits in the window −3 ≤ x ≤ 3, then shown in exact form where one exists.

x-intercepts (roots): None in this window
Local maxima: None in this window
Local minima: None in this window
Inflection points: (0, π/2)

Table of values

A few points to plot, with exact values where they are simple.

Values of arccos x
x	y = arccos x
−1	π
−√3/2	5π/6
−1/2	2π/3
0	π/2
1/2	π/3
√2/2	π/4
1	0

How to graph arccos x by hand

1
Plot the end points (−1, π) and (1, 0) and the middle point (0, π/2), using π ≈ 3.14.
2
Add (1/2, π/3) and (−1/2, 2π/3).
3
Draw a decreasing curve through them, vertical at both ends.