Download Graphs of the inverse trigs can be found here.

Section 6.6 extra: Graphs of Inverse Trig Functions
The main trigonometric functions sin(x), cos(x), and tan(x) are not one-to-one; they fail the Horizontal
Line Test largely because they keep repeating themselves periodically. That’s why the “inverse” trigonometric
functions only invert a portion of the graph where the function is one-to-one and has the same range:
• For sin(x) and tan(x), the portion from −π/2 to π/2 is used.1
Note that the sin(x) graph includes the ends, whereas the tan(x) graph excludes them. (You can’t include
an asymptote in the domain!)
• For cos(x), the portion from 0 to π is used (ends included).
Cosine decreases on this interval, instead of increasing, so arccos is the only decreasing inverse function.
• In each function, this domain is the only interval we can use that has all the range, contains 0, and has
the first quadrant in it. These restricted domains become the ranges of the inverse trig functions.
y = sin−1 (x) aka arcsin(x)
y = cos−1 (x) aka arccos(x)
• Increasing
• Decreasing
• Odd: arcsin(−x) = − arcsin(x)
• Neither even nor odd
• Domain: [−1, 1]
• Domain: [−1, 1]
• Range: [−π/2, π/2]
• Uses Quadrants I and IV (right half of unit circle), with negative values for Quadrant IV
• Range: [0, π]
• Uses Quadrants I and II (top half of unit circle)
y = tan−1 (x) aka arctan(x)
• Increasing
• Odd function: arctan(−x) = − arctan(x)
• Domain: (−∞, ∞)
• Range: (−π/2, π/2)
• Uses Quadrants I and IV (right half of unit circle), with negative values for Quadrant IV
• Two horizontal asymptotes: y = ±π/2
1 Compare this to problems from HW 5.5 & 5.6, where we had functions like f (x) = a + sin(bx) and f (x) = a + tan(bx). The
range for b was chosen specifically so that the angle θ we used would range from −π/2 to π/2!