Angles
Degrees and radians are two different units for measuring angles.
Degrees divide a full circle into 360 equal parts.
- A full circle = 360°
- A half circle (straight line) = 180°
- A right angle = 90°
Radians are based on the radius of a circle. One radian is the angle you get when you take the radius of a circle and wrap it around the circumference
s = r ( in radians).
- A full circle = 2π radians
- A half circle = π radians
- A right angle = π/2 radians
trigonometric functions of an acute angle
trigonometric functions
When we use a unit circle (radius = 1), the trigonometric ratios become much simpler:
- sin θ = y
- cos θ = x
- tan θ = y/x
This means the coordinates of any point on the unit circle are literally (cos θ, sin θ), which is elegant and easy to work with.
this also mean that
cos^2(θ) + sin^2(θ) = 1
cos(θ) = sin(θ+π/2)
Sine Sum Identities:
- sin(A + B) = sin A cos B + cos A sin B
- sin(A - B) = sin A cos B - cos A sin B
Cosine Sum Identities:
- cos(A + B) = cos A cos B - sin A sin B
- cos(A - B) = cos A cos B + sin A sin B