chapter 4 vocabulary
DESCRIPTION
Chapter 4 Vocabulary. Section 4.1 vocabulary. An angle is determined by a rotating ray (half-line) about its endpoint. . The starting point of the ray is the initial side of the angle. . The position of the ray after the rotation is the terminal side of the angle. . - PowerPoint PPT PresentationTRANSCRIPT
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Chapter 4 Vocabulary
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Section 4.1 vocabulary
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An angle is determined by a rotating ray (half-line) about its endpoint.
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The starting point of the ray is the initial side of the angle.
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The position of the ray after the rotation is the terminal side of the angle.
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The endpoint of the ray is the vertex of the angle.
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When an angle fits a coordinate system in which the origin is the vertex of the angle, and the initial side coincides with the positive x-axis that angle is in standard position.
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Positive angles are generated by counterclockwise rotation.
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Negative angles are generated by a clockwise rotation.
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Two angles that have the same initial and terminal sides are called coterminal angles.
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The measure of an angle is determined by the amount of rotation from the initial side to the terminal side.
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A central angle is an angle whose vertex is the center of the circle.
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One radian is the measure of a central angle Ѳ that intercepts an arc s equal in length to the radius r of the circle.
Ѳ = s / r , where Ѳ is measured in radians
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Angles between 0 and ∏ / 2 are called acute angles.
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Angles between ∏/2 and ∏ are called obtuse angles.
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A way to measure angles is in degrees where 1 degree is equivalent to a rotation of 1/360 of a complete revolution about the vertex.
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Complementary angles add to be 90 degrees or∏/2.
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Supplementary angles sum to equal 180 degrees or ∏.
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Linear speed
Linear speed = Arc length / time
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Angular speed
Angular speed = central angle/ time
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The unit circle Given by the equation : X2 + y2 = 1
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Definitions of Trigonometric functions
• Sin (t) = y• Cos(t) = x• Tan(t) = y/x• Csc(t) = 1/y• Sec(t) = 1/x• Cot(t) = x/y
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• A function f is periodic if there exists a positive real number c such that :
f(t + c) = f(t) For all t in the domain of f.The least number c for which f is
periodic is called the period of f.
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Even/ odd trig functions
Even • cos(-t) = cos(t)• sec(-t) = sec(t) odd• Sin(-t) = -sin(t) • tan(-t) = -tan(t) • csc(-t) = -csc(t) • cot(-t) = -cot(t)
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Section 4.3 Vocabulary
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Right triangle def. of Trig Functions
• Sin(Ѳ) = opp/hyp• Cos(Ѳ)= adj/hyp• Tan(Ѳ) = opp/adj• Csc(Ѳ) = hyp/opp• Sec(Ѳ) = hyp/adj• Cot(Ѳ) = adj/opp
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Sines of special angles
•Sin(30) =sin(∏/6) = ½•Sin (45) = sin(∏/4) = √2/2•Sin(60) = sin(∏/3) = √3/2
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Cosines of special angles
•Cos(30) = cos(∏/6) = √3/2•Cos(45) = cos(∏/4) = √2/2•Cos(60) = cos(∏/3) = ½
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Tangents of Special angles
• Tan(30) = tan(∏/6) = √3/3• Tan(45) = tan(∏/4) = 1• Tan(60) = tan(∏/3) = √3
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Reciprocal Identities• Sin(Ѳ) = 1/csc(Ѳ)• Cos(Ѳ) = 1/ sec(Ѳ)• Tan(Ѳ) = 1/cot(Ѳ)• Csc(Ѳ) = 1/sin(Ѳ)• Sec(Ѳ) = 1/cos(Ѳ)• Cot(Ѳ) = 1/tan(Ѳ)
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Quotient identities
• Tan(Ѳ) = sin(Ѳ) / cos(Ѳ)
• Cot(Ѳ) = cos(Ѳ) / sin(Ѳ)
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Pythagorean Identities
•Sin2(Ѳ) + cos2(Ѳ) = 1•1 + tan2(Ѳ) = sec2(Ѳ)•1 + cot2(Ѳ) = csc2(Ѳ)
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Angle of elevation
•The angle from the horizontal up to the object
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Angle of Depression
•The angle from the horizontal downward to the object.
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Section 4.4 Vocabulary
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Definitions of Trig Functions
Sin Ѳ = y/rcos Ѳ = x/rTan Ѳ = y/xCot Ѳ = x/ySec Ѳ = r/xCsc Ѳ = r/y
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Reference Angle• Let Ѳ be an angle in standard
position. Its reference angle is the acute angle Ѳ’ formed by the terminal side of V and the horizontal axis.
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Section 4.6 Vocabulary
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Amplitude • The amplitude of y = a sin(x) And y = a cos(x) Represents half of the distance
between the max and the min values of the function, and is given by
Amplitude = |a|
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Period• The b be a positive real
number. The period of y = a sin(bx) and t = a cos(bx) is given by
Period = 2∏/b
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Damping factor•In the function f(x) = x sin(x), the factor x is called the damping factor.
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Section 4.7 Vocabulary4
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Inverse sine functiony = sin (x) has a unique inverse
function called inverse sine function. It is denoted by
Y =arcsin(x) or y = sin-1 (x)
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Inverse cosine functiony = cos (x) has a unique inverse
function called inverse cosine function. It is denoted by
Y =arccos(x) or y = cos-1 (x)
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Inverse tangent functiony = tan (x) has a unique inverse
function called inverse tangent function. It is denoted by
Y =arctan(x) or y = tan-1 (x)