Download College Algebra Unit 9 Review Plan Trig - math-b

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College Algebra Unit 9 Review Plan Trig
(Geometry Text Chapter 9) Jan 2015
By the end of the 2 week unit a student should be able to:
Chapter 9
1) Be able to Utilize the GEOMETRIC MEAN to find missing sides of RIGHT
Triangles.
2) Utilize RATIO’s to find missing Sides of Right Triangles
3) Utilize Pythagorean Theorem to find missing sides of Right triangles
4) Understand Reference angle: θ is called THETA (Greek letter) for an angle
5) Understand Terminal side and how to measure Positive and Negative Angles
6) Utilize the Unit Circle to find:
a) Reference Points
b) Reference Angles
7) Know the THREE primary TRIG values for
a) 0 deg
30 deg
45 deg
b) Sin = 0.000 0.5000
0.7071
c) Cos = 1.000 0.8660
0.7071
d) Tan = 0.000 0.57735
1.0000
60 deg
0.8660
0.5000
1.7321
90 deg
1.0000
0.0000
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8) TRIGONOMETRIC RATIO’s
Given a right triangle with one angle and one side
a) Find the missing angles and missing side
b) A2 + B2 = C2  Adj2 + Opp2 = Hyp2
Hyp
c) SIN θ = Opp/ Hyp
Opp
θ
d) COS θ = Adj/ Hyp
Adj
e) TAN θ = Opp/ Adj
SIN
(30) = 1/2 (or 0.500)
9) Given a right triangle three sides
a) Find the missing angles
b) ARCSIN (Opp / Hyp ) = θ
c) ARCCOS (Adj / Hyp ) = θ
d) ARCTAN (Opp / Adj ) = θ
SIN-1
(1/2) = 30 degrees
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10) Find The area of a RIGHT-Triangle
a) BASIC Area = ½ (base) ( Height)
Height
Base
b) OTHER ways to Find Area if NOT a Right Triangle
A
c
Area = ½ bc{SIN (A)}
Area = ½ ac{SIN (B)}
b
B
C
a
11) HONORS Convert angles in Degree-minutes-seconds into Degrees Decimal
i. 30 deg – 15 min – 30 sec
ii. 30 deg + 15/60 + 30/3600 = 30 + .25 + 0.01 = 30.2501 degrees
12) HONIORS Find the true inverse trig functions
a) 1 /SIN = CSC
b) 1 / COS = SEC
c) 1 / TAN = COT
13) Utilize the Law of COSINE’s for a NON right Triangle to find
a) Find the missing angles and sides
In the Triangle find the missing sides and angles
A
c
c = a + b – 2ab*COS C
b2 = a2 + c2 – 2ac*COS B
a2 = c2 + b2 – 2cb*COS A
2
2
2
b
B
C
a
14) Utilize the Law of SINE’s for a NON right Triangle to find
a) Find the missing angles and sides
In the Triangle find the missing sides and angles
A
c
SIN (A) / a = SIN (B) / b = SIN (C) / c
b
B
C
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a
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Area = ½ ab{SIN (C)}
Area = ½ a2 {{SIN (B)* SIN(C)} / SIN(A)}
Area = ½ b2 {{SIN (A)* SIN(C)} / SIN(B)}
Area = ½ c2 {{SIN (A)* SIN(B)} / SIN(C)}
Finally...For ANY triangle with side lengths “a”, “b” and “c”
Area = √{s* (s-a) (s-b)(s-c)}
Where s = ½ * (a + b + c)
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HONORS GRAPHING SIN and COS
1) Plot the equations for a SIN or COS function
a)
f(x) = C + A SIN (Bx)
i. C = shift on the “Y” axis
= {MAX + MIN} /2
ii. A = Amplitude
= {MAX – MIN} /2
iii. B finds the period of the cycle = 2π / B
1. If B = 1 then the “normal” period is 2π
2. (a circles circumference)
iv. b = 2π / period
v. Graph the quarter periods
vi. Graph the MAX
vii. Graph the MIN
viii. Graph the “C”
ix. SIN starts at ZERO
x. COS Starts at MAX
xi.
f
= FREQUENCY {Cycles per unit time} = 1 /P = 1 / {2π / B}
Graph the equation f(Ψ) = Y = 2 + 4 * SIN ({1/4}Ψ)
Graph the equation f(Ψ) = Y = 2 + 4 * COS ({1/4}Ψ)
COS MAX
+4 (6)
EQ
MIN
EQ
8π* 1/4
2π MAX
8π * 1/2
4π EQ
MAX
2
-4 (-2)
SIN EQ
8π * 3/4
6π MIN
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8π PERIOD
8π EQ