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# Trigonometry Ch 1

TermDefinition
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.
Created by: drjolley