Trig SubstitutionWhich substitution clears which square root, and what it leaves behind.MathematicsTake a > 0 and θ in the principal range.ExpressionSubstituteBecomes√(a² − x²)x = a sin θa cos θ√(a² + x²)x = a tan θa sec θ√(x² − a²)x = a sec θa tan θa² + x², no rootx = a tan θa² sec² θx² + bx + cComplete the squareThen use a row aboveConvert back with a right triangle, not by inverting the substitutionblindly. sin θ = x/a fixes every other ratio at once.Trig Substitutionlearnposters.com
Trig Substitution — printable math wall chart from LearnPosters. Free vector PDF, US Letter and A4.

What’s on the Trig Substitution poster

A 5-row table: Expression · Substitute · Becomes.

Take a > 0 and θ in the principal range.

Convert back with a right triangle, not by inverting the substitution blindly. sin θ = x/a fixes every other ratio at once.

Questions about the Trig Substitution poster

What’s on the Trig Substitution poster?
A 5-row table: Expression · Substitute · Becomes. Take a > 0 and θ in the principal range. √(a² − x²) — x = a sin θ — a cos θ; √(a² + x²) — x = a tan θ — a sec θ; √(x² − a²) — x = a sec θ — a tan θ; a² + x², no root — x = a tan θ — a² sec² θ; x² + bx + c — Complete the square — Then use a row above. Convert back with a right triangle, not by inverting the substitution blindly. sin θ = x/a fixes every other ratio at once.
Who is the Trig Substitution poster for?
Trig Substitution belongs to the Mathematics section rather than to a school year, because math is not something one grade owns. Anyone learning calculus can pin it up — a beginner, a student mid-course, or someone revising years later.
When should you use the Trig Substitution poster?
When the integrand contains a square root of a sum or difference of squares. A wall chart earns its place by being glanceable from where the work is happening, so Trig Substitution belongs on the wall where that math work actually happens, within glancing distance, rather than filed away.
What other posters go with Trig Substitution?
The Chain Rule, Derivative Rules and Fundamental Theorem sit alongside Trig Substitution in the Mathematics section. Printed together they make a wall rather than a single sheet, which is how a reference set actually gets used.The Chain RuleDerivative RulesFundamental Theorem
Is the Trig Substitution poster free to download and print?
Yes. Trig Substitution downloads as a free PDF with no account, no email and no watermark, like everything else in the Mathematics section. Print as many copies as you like for a home, a classroom, a library or a tutoring group; reselling the file is the only thing the licence rules out.Read the licence
What size does the Trig Substitution poster print at?
Trig Substitution is a vector PDF laid out for US Letter, and prints on A4 with Fit to page — the same file, no separate download. Because every mark on it is drawn rather than photographed, it stays sharp enlarged to A3, A2 or A1 at a copy shop. Colour carries emphasis only, so a greyscale print of Trig Substitution loses nothing.Printing guide

Related posters

Charts that sit alongside Trig Substitution on the same wall.

Browse every Mathematics poster, or start from the full catalogue.