Converting Radians& Degrees
Radian Measure to Degree Measure
π/3
60 degrees
(1,1)
sinθ
Amp of y=sinx
1
The minute hand of a clock moves from 12 to 2 o’clock, or 1/6 of a complete revolution. Through how many degrees does it move? Through how many radians does it move?
60 degrees/ 𝛑/3 radian
Radian Measure to Degree Measure
4π/3
240 degrees
(-1/2,√3/2)
sint=√3/2 cost=-1/2 tant=-√3 csct=2√3/3 sect=-2 cot=-√3/3
cosθ
a/h
Period of y=sinx
2𝝅
The graph of y = A sin Bx has amplitude = ? and period = ?.
A, B
Radian Measure to Degree Measure
13π/6
390 degrees
t=𝝅/2
sint=1 cost=0 tant=und. csct=1 sect=und. cott=0
tanθ
o/a
Amp of y=9987cosx
9987
A region that is 30 north of the Equator averages a minimum of 10 hours of daylight in December. Hours of daylight are at a maximum of 14 hours in June. Let x represent the month of the year, with 1 for January, 2 for February, 3 for March, and 12 for December. If y represents the number of hours of daylight in month x, use a sine function of the form y = A sin(Bx - C) + D to model the hours of daylight.
y= 2 sin (30x-90) + 12
Radian Measure To Degree Measure
7π/4
315 degrees
t=𝝅/4
sint=√2/2 cost=√2/2 tant=1 csct=√2 sect=√2 cott=1
cscθ
h/o
Period of y=23423sin2x
A plane takes off at an angle of 6°. After traveling for one mile, or 5280 feet, along this flight path, find the plane’s height, to the nearest tenth of a foot, above the ground. (Round up to nearest whole unit)
552
Radian Measure to Degree Measure
4π/12 ( to the nearest whole unit)
60 degrees
cos(-𝝅/4)
√2/2
secθ
Period of y=tanx
𝝅
A tree that is 50 feet tall casts a shadow that is 60 feet long. Find the angle of elevation, to the nearest degree, of the sun. (Round to nearest whole unit)
40 degrees