AP Precalc Special Right Triangle Rules + Unit Circle Radian Measures

What does Syr-Cxr-Tyx stand for?

Sine of theta= y/r… Cosine of theta= x/r… Tangent of theta= y/x

Pythagorean Theorem

leg squared + leg squared = hypotenuse squared

30-60-90 Right Triangle Rule

The side length opposite the 30 angle (short leg) is “a,” the side length opposite the 60 angle (long leg) is “a root3,” the side length opposite the 90 angle (hypotenuse) is “2a”

45-45-90 Right Triangle Rule

The side lengths opposite the 45 angles (both legs) are “a,” and the side length opposite the 90 angle (hypotenuse) is “a root 2”

Denominator of 6

Closest to x-axis (initial ray)

Denominator of 4

In the middle of each quarter arc length

Denominator of 3

Vertically the furthest from x-axis (closest to y-axis)

Order of the 4 quarter measures

0/2pi, pi over 2, pi, 3pi over 2, back to start

Quadrant I Rule

Numerator is always just 1 pi, and denominator follows the 6,4,3 pattern

Quadrant II Rule

Numerator is one LESS than denominator (d-1), and denominator follows 6,4,3 pattern

Quadrant III Rule

Numerator is one MORE than denominator (d+1), and denominator follows 6,4,3 pattern

Quadrant IV Rule

Numerator is DOUBLE denominator MINUS 1 (2d-1), denominator follows 6,4,3 pattern