Geometry and Trigonometry
Five topics covering the SAT's Geometry and Trigonometry domain end to end. Lines, angles, and triangles, right triangles, right-triangle trigonometry, circles, and area and volume. The errors here are setup errors: the wrong angle rule, a misplaced hypotenuse, a ratio built from the wrong sides, a diameter posing as a radius.
Topics
Reference The triangle, circle, and trig facts behind every problem in this unit
Right triangle (hypotenuse sits alone)
$a^{2} + b^{2} = c^{2}$
Special triangles (from the short side)
$x,\ x,\ x\sqrt{2} \quad\text{and}\quad x,\ x\sqrt{3},\ 2x$
Trig ratios (from the named angle)
$\sin = \dfrac{\text{opp}}{\text{hyp}},\ \cos = \dfrac{\text{adj}}{\text{hyp}},\ \tan = \dfrac{\text{opp}}{\text{adj}}$
Cofunction (complements, through 90)
$\sin x^{\circ} = \cos(90 - x)^{\circ}$
Circle (radius, never diameter)
$A = \pi r^{2}, \quad C = 2\pi r, \quad (x - h)^{2} + (y - k)^{2} = r^{2}$
Arc and sector (share of the right whole)
$\dfrac{\theta}{360}\cdot 2\pi r \quad\text{and}\quad \dfrac{\theta}{360}\cdot \pi r^{2}$
Unit 5 tools