An angle is an opening that is measured in degrees. A radian is a measurement where the radius is the same length as the arc length
Summary: A degree is a unit of measurement and a radian is the measure of the central angle whose arc has the length to the circle's radius. Degrees can be converted into radians and radians into degrees as well.
How to measure in both degrees and Radians
A degree is unit of measurement which is represented by the symbol (°). for angles and arcs.
A radian is the measure of a central angle whose intercepted arc has a length equal to the circle's radius.
Degrees can be converted into radians and radians into degrees.
Summary: In order to convert from degrees to radians you must multiply by pi over 180 degrees. The degrees cancel out and then you simplify.
The conversion between degrees and radian
To convert radians to degrees, multiply by
180°/ π radians.
To convert degrees to radians, multiply by
π radians/ 180°.
Ex 1: Convert 200° into radian measure: 200°⋅π/180° =10π/9 radians =3.49 radians
Ex 2: Convert 49π radians to degrees 4π/9⋅180°/π =4π⋅180°/9π=720°π/9π =720°π⋅/9π (π cancels out) =80°
Sine and cosine
Sine: On a unit circle sine is y On a unit circle sine is on quadrants I and IV Period is 2π Its graph begins at zero.
Cosine: The function y=cos x Summary: On a unit circle cosine is x On a unit circle cosine is on quadrants I and II Period is 2π Its graph begins at one.
Ex:1Ex:2 Cos45°=√2/2 Sin45°= √2/2
Period: Is a full cycle The part where a cosine or sine graph goes back to the starting point. Equation: 2π/│b│
Frequency: Reciprocal of the period Equation:│b│/2π
Angle of Elevation: The angle from the eyesight horizontally moving up looking at something above
Angle of Depression: The angle from the eyesight horizontally moving down looking at something below Ex:1 Using Angle of Depression The angle of depression of a buoy from the top of the Bay lighthouse 130 ft above the surface of the water is 6°. Find the distance x from the base of the lighthouse to the buoy.
tanθ=tan6°=130/x x=130/tan 6°= 1236.9
Summary: With an angle of elevation you could find how tall something above the ground is without having to measure it. With an angle of depression you could find how tall something below the ground is.
Co-terminal Angles: two angles in the same angle-measurement that can have the same starting side and ending side Ex:1 Find a positive angle that is co-terminal 30° Add 360°: 30°+360°=390°