Chapter 3: Radian Measure
Chord
For very small angles, the length of the arc is approximately equal to the length of the chord.
360
How many degrees is 2πrad?
300
How many degrees is 5π/3?
225
How many degrees is 5π/4?
150
How many degrees is 5π/6?
315
How many degrees is 7π/4?
90
How many degrees is π/2?
45
How many degrees is π/4?
30
How many degrees is π/6?
180
How many degrees is π?
0
How many radians is 0°?
2π/3
How many radians is 120°?
3π/4
How many radians is 135°?
πrad
How many radians is 180°
7π/6
How many radians is 210°?
4π/3
How many radians is 240°?
3π/2
How many radians is 270°?
11π/6
How many radians is 330°?
π/3
How many radians is 60°?
Definition III
If (x,y) is any point on the unit circle, and t is the distance from (1,0) to (x,y) along the circumference of the unit circle, then: - cos(t) = x - sin(t) = y - tan(t) = y/x - cot(t) = x/y - csc(t) = 1/y - sec(t) = 1/x
Radius
If a central angle in a circle cuts off an arc equal in length to the __________, it has a measure of 1 radian.
s/r
If a central angle, θ, in a circle of radius, r, cuts off an arc of length, s, then θ, in radians, is:
1/2r²θ
If θ (in radians) is a central angle in a circle with radius r, then the area of the sector formed by angle θ is given by: A=?
rθ
If θ (in radians) is a central angle in a circle with radius r, then the length of the arc cut off by θ is given by: S=?
θ
If θ terminates in QI, then θ's reference angle is:
180°-θ
If θ terminates in QII, then θ's reference angle is:
θ-180°
If θ terminates in QIII, then θ's reference angle is:
360°-θ
If θ terminates in QIV, then θ's reference angle is:
Real
Radians are unitless. They are ______ numbers.
Proportional
The Arc Length is _________ to the Central Angle
Reference Angle
The ____________ _________ for any angle in standard position is the positive acute angle between the terminal side of θ and the x-axis.
Calculator
To find trigonometric functions without exact values, use a ___________ to approximate the value.
False
True or False? The trigonometric function of an angle and its coterminal angles are never equal.
True
True or false? The trigonometric function of an angle and its reference angle are the same except sometimes sign.
1
What is the cos(0°)?
√3/3
What is the cot(π/3)?
kπ
What is the domain of cot(t) and csc(t)
(-∞,∞)
What is the domain of sin(t) and cos(t)
π/2+kπ
What is the domain of tan(t) and sec(t)
(-∞,-1]∪[1,∞)
What is the range of sec(t) and csc(t)
[-1,1]
What is the range of sin(t) and cos(t)
(-∞,∞)
What is the range of tan(t) and cot(t)
1/2
What is the sin(π/6)?
1
What is the tan(45°)?
Degree
When approximating values of trigonometric functions, make sure the calculator is set to ________ mode.
Radian Measure
______ _______ provides real numbers for calculations rather than degrees.
