Inverse Cosine
Angle whose cosine is x, range [0, π].
Key idea
Angle whose cosine is x, range [0, π].
In depth
arccos x gives the angle in [0, π] whose cosine is x. Its domain is [−1, 1]. Note arcsin x + arccos x = π/2.
Worked example
arccos(0) = π/2. arccos(−1/2) = 2π/3.
Formula
Real-world uses
- Finding the angle between two vectors in physics, such as the angle between two forces
Common mistake
Giving an angle outside [0, π].
How to learn this
- Read the key idea and say it in your own words.
- Work through the worked example, then try a similar problem.
- Use the interactive lesson’s visual and mini-quiz to check the pattern.
Frequently asked questions
What is Inverse Cosine?
Angle whose cosine is x, range [0, π]. It is a topic at the advanced level in Trigonometry.
What is the formula for Inverse Cosine?
The key formula is y = arccos x.
Where is Inverse Cosine used in real life?
Real-world examples: Finding the angle between two vectors in physics, such as the angle between two forces.
What should I learn before Inverse Cosine?
Make sure you are comfortable with Inverse Sine, the previous topic in Trigonometry.
What is a common mistake with Inverse Cosine?
Giving an angle outside [0, π].
How can I practise Inverse Cosine?
Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.
What comes after Inverse Cosine?
Move on to Inverse Tangent next.
Related advanced topics in Trigonometry
- Graph of Tangent – Periodic with vertical asymptotes at odd multiples of π/2.
- Phase Shift – Horizontal translation of a wave.
- Vertical Shift and Midline – Moves the wave up or down.
- General Sinusoid – Combine amplitude, period, phase and shift.
- Graphs of Reciprocal Trig Functions – Secant, cosecant and cotangent graphs.
- Pythagorean Identity – The key identity from the unit circle.