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