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.
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.
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