Trigonometry of unit circle
As θ increases from 0⁰ to 90⁰, what happens to the length of the radius?
the length of the radius does not change
cos (30°)
√3/2 = 0.866
sin (60°)
√3/2 = 0.866
cos (0°)
√4/2 = 1
sin (90°)
√4/2 = 1
at what angle b/t 0° and 90° is cosine the longest?
it is longest at 0°
at what angle b/t 0 and 90 is cosine the shortest?
it is shortest at 90°
b/t 0° and 90°, what angle is sine the longest
it is the longest at 90°
b/t 0° and 90°, what angle is sine the shortest?
it is the shortest at 0°
As θ increases from 0° to 90° what happens to the length of the run aka cos (θ) ?
cos (θ) decreases - the cosine is the run, therefore the cosine decreases as the theta increases from 0 to 90.
As θ increases from 0 to 90, what happens to the length of the rise, aka the sin(θ) line?
the sin (θ) increases - sine is the rise, thus the rise increases as theta approaches 90
sin (0⁰)
√0/2
cos (90°)
√0/2 = 0
cos (60°)
√1/2 = 0.5
sin (30°)
√1/2 = 0.5
cos (45°)
√2/2 = 0.707
sin (45°)
√2/2 = 0.707