1/10
3.2 · sin Definition
sin θ = ? for a circle of radius r with terminal ray at P(x,y)
sin θ = ?
Vertical or horizontal displacement?
2/10
3.2 · cos Definition
cos θ = ? for a circle of radius r with terminal ray at P(x,y)
cos θ = ?
Vertical or horizontal displacement?
3/10
3.2 · tan — Two Forms
Write BOTH formulas for tan θ
Slope AND ratio of sin/cos
4/10
3.2 · Unit Circle
On the unit circle (r=1), what do sin θ and cos θ simplify to?
Plug r=1 into the general formulas
5/10
3.2 · Reflections
P=(x,y) in Q1. Give coordinates of Q (y-axis), R (origin), S (x-axis)
Which coordinate flips for each?
6/10
3.2 · tan = slope
Terminal ray lies along y = mx. What is tan θ, and why?
No calculation needed
7/10
3.2 · Radian Definition
What is the radian measure of an angle in standard position?
θ = ?
Ratio involving arc length and radius
8/10
3.2 · Full Revolution
How many radians in one full revolution?
C = 2πr
2/10
✓ cos Definition
cos θ = x/r
HORIZONTAL displacement ÷ radius. x is the horizontal coordinate of P. cos = left/right = x.
1/10
✓ sin Definition
sin θ = y/r
VERTICAL displacement ÷ radius. y is the vertical coordinate of P. sin = up/down = y.
4/10
✓ Unit Circle (r=1)
sin θ = y · cos θ = x
With r=1: sin=y/1=y and cos=x/1=x. Every unit circle point gives trig values as its coordinates directly.
3/10
✓ tan — Two Forms
tan θ = y/x AND sin θ / cos θ
tan = slope of the terminal ray. Both forms equivalent since y/x = (y/r)÷(x/r) = sin/cos.
6/10
✓ Reflections
Q=(−x, y) · R=(−x, −y) · S=(x, −y)
Q: y-axis flip → x becomes −x. R: origin flip → both negative. S: x-axis flip → y becomes −y.
5/10
✓ tan = slope
tan θ = m (the slope of the line)
Terminal ray through origin with slope m. tan = y/x = rise/run = SLOPE. Always.
8/10
✓ Full Revolution
2π radians
From C = 2πr: θ = 2πr/r = 2π. One full circle = 2π. Half = π. Quarter = π/2. Clockwise = negative.
7/10
✓ Radian Definition
θ = arc length / r
Radian = arc length created by the angle on a circle of radius r, divided by r.
10/10
✓ Example 7 Method
sub y=−3x → 10x²=r² → x=−r/√10 (Q2) → sin=3/√10, cos=−1/√10, tan=−3
Step 1: y=−3x into x²+y²=r² gives x=±r/√10. Step 2: Q2 so x negative. Step 3: y=3r/√10.
9/10
✓ Fraction to Radian
θ = (3/4) × 2π = 3π/2
General: θ = fraction × 2π (positive=CCW, negative=CW). So 3/4 × 2π = 6π/4 = 3π/2.