Term | Definition |
A ray is defined as ___. | a point on a line together with all points of the line on one side of that point |
An angle is defined as ___. | the union of two rays with a common endpoint |
The common endpoint of an angle is called the ___. | vertex |
The fixed ray of an angle is the ___ side. | initial |
The rotated ray of an angle is the ___ side. | terminal |
An angle whose vertex is the center of a circle is called the ___ angle. | central |
The arc through which the terminal side of a central angle moves is called the ___. | intercepted arc |
An angle located in a Cartesian coordinate system with the vertex at the origin and initial side on the x axis is said to be in ___. | standard position |
An angle is denoted with ___. | α, β, etc. |
The measurement of an angle is denoted with ___. | m(α) |
1/360 of a circle is a ___. | degree |
A positive angle goes ___ and a negative angle goes ___. | counterclockwise, clockwise |
0>m(α)>90 is called a/an ___ angle. | acute |
m(α)=90 is called a/an ___ angle. | right |
90>m(α)>180 is called a/an ___ angle. | obtuse |
m(α)=180 is called a/an ___ angle. | straight |
An angle in standard position is said to lie in the quadrant where ___. | its terminal side lies |
A ___ angle has its terminal side on an axis. | quadrantal |
T or F? Straight and right angles are quadrantal angles. | T |
Two angles whose terminal angles are in the same position are called ___ angles. | coterminal |
Coterminal measures differ by multiples of ___ degrees. | 360 |
Coterminal angle: m(β) = m(α) + ___ where k = ___. | k360, number of rotations |
Which quadrant is bottom left? | III |
Each degree is divided into ___ equal parts called ___. | 60, minutes |
Each minute is divided into ___ equal parts called ___. | 60, seconds |
A second is what fraction of a degree? | 1/3600 |
What angle is 59°59'60"? | 60° |
A circle with a radius of 1 (no unit) is called a ___. | unit circle |
The circumference (C) of a unit circle is defined by the formula ___. | 2π (C = 2πr = 2π(1) = 2π) |
The radian measure is the measure of ___. | the intercept arc directed length |
Directed length means the length is either ___ or ___. | positive, negative |
m(α)= ___ radians | s |
2π rad = ___° | 360 |
π rad = ___° | 180 |
360° = ___ rad (digits) | 6.28 |
180° = ___ rad (digits) | 3.14 |
The arc length formula is ___. | s = αr (s=arc length, α=radians, r=radius) |
Area of a sector formula is ___. | A = (αr²)/2 |
For an object moving in a circle, there are 2 types of velocity; ___ velocity and ___ velocity. | angular, linear |
For one revolution an object moves ___ radians. | 2π (6.28) |
We express angular velocity in ___ per unit of time. | radians |
T or F? Angular velocity and linear velocity are unrelated. | True. Angular velocity is only concerned with revolutions per time not the linear speed of the object. |
Angular velocity is given by the formula ___. | ω = α/t (e.g., rpm, rad/sec, rad/min, degrees/hour, etc.) |
Linear velocity in a circle is given by the formula ___. | v = s/t (i.e., v = d/t) or v = αr/t (where s = αr) |
Linear velocity in terms of angular velocity is given by the formula ___. | v = rω (v = αr/t, v = r(α/t)) |
sin = ___ | y/r (opp/hyp) (NOTE: r = hypotenuse not radius!) |
cos = ___ | x/r (adj/hyp) |
tan = ___ | y/x (opp/adj) |
csc = ___ | r/y (hyp/opp) |
sec = ___ | r/x (hyp/adj) |
cot = ___ | x/y (adj/opp) |
Since x = 0 for any point on the y-axis, ___ and ___ are undefined for any angle that terminates on the y-axis. | tan, sec |
Since y = 0 for any point on the x-axis, ___ and ___ are undefined for any angle that terminates on the x-axis. | csc, cot |
Trig functions are ___. | ratios |
The reciprocal of sin is ___. | csc |
The reciprocal of cos is ___. | sec |
The reciprocal of tan is ___. | cot |
1/(sin α) = ___. | csc |
1/(cos α) = ___. | sec |
1/(tan α) = ___. | cot |
T or F? Angles of the same proportion, regardless of size, will have the same values for the trig fxns. | True |
sin 30 = ___. | 1/2 |
cos 30 = ___. | √3/2 |
tan 30 = ___. | √3/3 |
sin 45 = ___. | √2/2 |
cos 45 = ___. | √2/2 |
tan 45 = ___. | 1 |
sin 60 = ___. | √3/2 |
cos 60 = ___. | 1/2 |
tan 60 = ___. | √3 |
What is the mnemonic for remembering the sign of a fxn in each quadrant? What does it mean? | All students take calculus. All are (+) in Quad I, sin and csc are (+) in II, tan and cot are (+) in III, cos and sec are (+) in IV |
If an angle lies in quadrant II, the sec will be ___ (+ or -). | (-) |
If an angle lies in quadrant III, the cot will be ___ (+ or -). | (+) |
If an angle lies in quadrant IV, the sec will be ___ (+ or -). | (+) |
sin-¹(1/2) = ___. | 30° |
sin-¹(√2/2) = ___. | 45 |
sin-¹(√3/2) = ___. | 60 |
cos-¹(1/2) = ___. | 60 |
cos-¹(√2/2) = ___. | 45 |
cos-¹(√3/2) = ___. | 30 |
tan-¹(√3/3) = ___. | 30 |
tan-¹(1) = ___. | 45 |
tan-¹(√3) = ___. | 60 |
csc 30 = ___. | 2 |
csc 45 = ___. | √2 |
csc 60 = ___. | 2√3/2 |
sec 30 = ___. | 2√3/3 |
sec 45 = ___. | √2 |
sec 60 = ___. | 2 |
cot 30 = ___. | √3 |
cot 45 = ___. | 1 |
cot 60 = ___. | √3/3 |
x coordinates on the unit circle are the ___ of the angle. | cos |
y coordinates on the unit circle are the ___ of the angle. | sin |
Radians measure ___ around the circle and degrees measure ___. | arc length of the unit circle, angles |
Besides y/x, the tan of an angle can also be calculated by the ___/___. | sin/cos |
Besides x/y, the tan of an angle can also be calculated by the ___/___. | cos/sin |
The sum of the angles of a triangle always equals ___°. | 180 |
The angle of ___ for a point is the angle between the observer and the ground to a point ABOVE the gound. | elevation |
The angle of ___ for a point is the angle between a vector from the observer to a point BELOW the observer and a horizontal line parallel with the ground at the level of the observer. | depression |
The Fundamental Identity of trig is the equation ___. | sin² α + cos² α = 1 |
The Fundamental Identity solved in terms of cos is ___. | sin α = ±√(1 - cos² α) |
The Fundamental Identity solved in terms of sin is ___. | cos α = ±√(1 - sin² α) |
For any nonquadrantal angle, the ___ angle for θ is the positive acute angle θ' formed by the terminal side and the nearest x-axis. | reference |
T or F? The sin, cos, tan, etc. of any angle is the same as the reference angle aside from possibly the sign. | True |
T or F? The angle of elevation and the angle of depression are always equal if there is an observer at the ground and at the top. | True. The angle of depression is between a downward vector and a horizontal line that is parallel to the ground. It is NOT between the downward vector and the vertical line. |
T or F? The angle of depression is NOT made suing the vertical line. | True. It is with a horizontal line parallel with the ground. |