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