SAT Geometry and Trigonometry: what your AP classes already cover

Area and volume, lines, angles and triangles, right-triangle trigonometry and circles. AP courses use these facts constantly but rarely teach them directly, so this domain is where a quick review helps most.

Each row is one SAT Geometry and Trigonometry skill and the AP units on this site where you already practice it. Revisit those notes, then work through the two examples below before opening the answers.

Geometry and Trigonometry skills, matched to AP units

SAT skill	Where it comes up in AP	Why it carries over
Area and volume	AP Calculus AB, Unit 8	Area and volume formulas are the cross sections you integrate in Calculus Unit 8.
Lines, angles, and triangles	AP Precalculus, Unit 3	Angle facts and similar triangles sit underneath every unit-circle argument.
Right triangles and trigonometry	AP Precalculus, Unit 3	Sine, cosine and tangent from right triangles, extended to the unit circle.
Circles	AP Precalculus, Unit 3 AP Precalculus, Unit 4	Radians, arc length and the equation of a circle; Unit 4 traces circles parametrically.

Worked example 1: Right triangles and trigonometry

In a right triangle, \(\sin A=\frac{5}{13}\) for an acute angle \(A\). What is \(\cos A\)?

Show the answer and working

Answer: \(\frac{12}{13}\)

The sides are in the ratio \(5:12:13\), since \(5^2+12^2=13^2\). So \(\cos A=\frac{12}{13}\), the same as using \(\sin^2A+\cos^2A=1\) from AP Precalculus Unit 3.

Worked example 2: Circles

What is the radius of the circle \(x^2+y^2+8x-6y=0\)?

Show the answer and working

Answer: 5

Complete the square: \((x+4)^2+(y-3)^2=16+9=25\), so the center is \((-4,3)\) and the radius is \(5\).