Inverse Tangent
Angle whose tangent is x, range (−π/2, π/2).
Key idea
Angle whose tangent is x, range (−π/2, π/2).
In depth
arctan x gives the angle in (−π/2, π/2) whose tangent is x. It accepts any real number and approaches ±π/2 as x → ±∞. It is used to find angles from slopes.
Worked example
arctan(1) = π/4. A slope of 3 corresponds to arctan 3 ≈ 71.6°.
Formula
Real-world uses
- Calculating the direction of a line from its slope, such as a compass bearing from coordinates
Common mistake
Ignoring the quadrant when converting coordinates; use atan2 for full angles.
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 Tangent?
Angle whose tangent is x, range (−π/2, π/2). It is a topic at the advanced level in Trigonometry.
What is the formula for Inverse Tangent?
The key formula is y = arctan x.
Where is Inverse Tangent used in real life?
Real-world examples: Calculating the direction of a line from its slope, such as a compass bearing from coordinates.
What should I learn before Inverse Tangent?
Make sure you are comfortable with Inverse Cosine, the previous topic in Trigonometry.
What is a common mistake with Inverse Tangent?
Ignoring the quadrant when converting coordinates; use atan2 for full angles.
How can I practise Inverse Tangent?
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 Tangent?
Move on to Trig and Inverse Trig Compositions 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.