Inverse Trigonometric Functions — Drills
Inverse Trigonometric Functions has 5 drill skills. Each one generates fresh questions every time, with a hint and full worked steps, so you can keep practising a single skill until it settles.
What these drills cover
These questions use 12 ideas from the course. Follow any of them for a definition, where it is taught, and what it leads to.
- Repeating — Every fraction becomes a decimal that either stops or repeats forever.
- Function — A rule pairing each input with exactly one output.
- Range — The set of outputs that actually occur.
- Adjacent — The side next to that angle which is not the hypotenuse.
- Sine — sin θ = oppositehypotenuse.
- Cosine — cos θ = adjacenthypotenuse.
- Composition — Running one function on the output of another, written (f ° g)(x) = f(g(x)).
- Reference angle — The acute angle between the terminal side and the x-axis.
- Arcsine — The inverse of sine, restricted to outputs from -90° to 90°.
- Arccosine — The inverse of cosine, restricted to outputs from 0° to 180°.
- Arctangent — The inverse of tangent, restricted to outputs strictly between -90° and 90°.
- Quadrant — One of the four regions the axes divide the plane into.
Value
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Find arccos 12 in degrees.
Worked answer
60
cos 60° = 12
Problem 2
Find arccos √32 in degrees.
Worked answer
30
cos 30° = √32
Negatives
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Find arcsin(-√22) in degrees.
Worked answer
-45
Reference angle 45°
Negative, so -45°
Problem 2
Find arccos(-√32) in degrees.
Worked answer
120
Reference angle 60°
Quadrant II: 180-60 = 120°
Obtuse
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
An obtuse angle has sin A = 0.454. Find A to the nearest degree.
Worked answer
153
sin-1(0.454) ≈ 27°
Obtuse: 180-27 = 153°
Problem 2
An obtuse angle has sin A = 0.6561. Find A to the nearest degree.
Worked answer
139
sin-1(0.6561) ≈ 41°
Obtuse: 180-41 = 139°
Composing functions
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Evaluate arcsin(sin 225°) in degrees.
Worked answer
-45
Reference angle 45°
Sine is negative there, so the answer is -45°
Problem 2
Evaluate arcsin(sin 120°) in degrees.
Worked answer
60
Reference angle 60°
Sine is positive, so the answer is 60°
Range
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
What is the range of arccos?
- -90° to 90°
- 0° to 180°
- 0° to 360°
- 0° to 90°
Worked answer
0° to 180°
Cosine falls from 1 to -1 across 0° to 180°
Problem 2
What is the range of arctan?
- -90° to 90°
- 0° to 180°
- 0° to 360°
- 0° to 90°
Worked answer
-90° to 90°
That stretch covers the full range without repeating