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Ch 8 Concept Workshop
Know the basics of right triangle
trigonometry
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S-O-H C-A-H T-O-A
Extending the Sine and cosine
functions to all angles
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An angles’ intersection with the unit circle
(Sin: y value, cos: x value)
Know how to graph a sine function.
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Periodic (360 degrees), starts at 0, crosses
the origin, crosses the x axis at 180n
Know how to graph a cosine function.
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Periodic (360 degrees), starts at maximum
value (1), crosses the x axis at 90+180n
Know how to graph a tangent
function.
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Periodic (180 degrees), asymptotes
whenever cos = 0, shaped like a cubic
function
Understand what it means to be a
periodic function.
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Repeats a set value of numbers in a
specific period of time
Assignment that reinforces the
concept
Can extend the definition of tangent
function to fit any angle.
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tan x = sin x / cos x
Know the sign of sine, cosine and
tangent in each quadrant.
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Understands how to use inverse
trigonometric functions to find the
value of needed.
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Q1 - all (sin +, cos +, tan +)
Q2 - students (sin +, cos -, tan -)
Q3 - take (sin -, cos -, tan +)
Q4 - calculus (sin -, cos +, tan -)
When sin x = # then inverse sin of # = x
(Inverse sin and cos only have solutions
when the ratio # is between -1 and 1)
(Inverse tan has solutions for all real #)
Can use a reference angle to find the
value of a given angle.
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The acute angle formed by the terminal
side of the original angle and the x axis
Understand that there are multiple
solutions to n=sine  .
Can solve equations using
trigonometric functions.
Understand the relationship between
the unit circle and the Pythagorean
Theorem.
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Find the reference angle, determine the
quadrant that has the correct sign
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sin^2 + cos^2 = 1
Knows the complementary Identities
and can reason logically to prove.
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sin (90-x) = cos x
cos (90-x) = sin x
(tan (90-x) = 1/tan x)
Knows the supplementary Identities
and can reason logically to prove.
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sin (180-x) = sin x
cos (180-x) = -cos x
(tan (180-x) = -tan x)
Knows the opposite angle Identities
and can reason logically to prove.
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sin (-x) = -sin x
cos (-x) = cos x
tan (-x) = -tan x
Knows the exact value of angles from
0 to 360.
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Know the sin of a sum or difference
And can use it to find exact values of
angles.
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Cos θ Sinθ
Tanθ
θ
0
30
45
60
90
180
270
360
sin (A+B) = sinAcosB + sinBcosA
sin (A-B) = sinAcosB - sinBcosA
Know the cosine of a sum or
difference.
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Cos (A+B) = cosAcosB - sinAsinB
Cos (A-B) = cosAcosB + sinAsinB