Graph of Tangent
Periodic with vertical asymptotes at odd multiples of π/2.
Key idea
Periodic with vertical asymptotes at odd multiples of π/2.
In depth
y = tan x has period π and vertical asymptotes at x = π/2 + kπ, where cos x = 0. It rises through zero between asymptotes. It is not bounded.
Worked example
tan(π/4) = 1, tan(−π/4) = −1, and tan x → ∞ as x → π/2 from the left.
Formula
Real-world uses
- Modelling slopes that become steep, such as a sliding gate or a ramp near vertical
Common mistake
Drawing the graph through the asymptotes.
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 Graph of Tangent?
Periodic with vertical asymptotes at odd multiples of π/2. It is a topic at the advanced level in Trigonometry.
What is the formula for Graph of Tangent?
The key formula is y = tan x.
Where is Graph of Tangent used in real life?
Real-world examples: Modelling slopes that become steep, such as a sliding gate or a ramp near vertical.
What should I learn before Graph of Tangent?
Make sure you are comfortable with Graph of Cosine, the previous topic in Trigonometry.
What is a common mistake with Graph of Tangent?
Drawing the graph through the asymptotes.
How can I practise Graph of 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 Graph of Tangent?
Move on to Amplitude next.
Related advanced topics in Trigonometry
- 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.
- Other Pythagorean Identities – Divide the identity by sin² or cos².