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R Y G Explanation and/or definition
Ch 8 Concept Workshop
Know the basics of right triangle
trigonometry
x
S-O-H C-A-H T-O-A
Extending the Sine and cosine
functions to all angles
x
An angles’ intersection with the unit circle
(Sin: y value, cos: x value)
Know how to graph a sine function.
x
Periodic (360 degrees), starts at 0, crosses
the origin, crosses the x axis at 180n
Know how to graph a cosine function.
x
Periodic (360 degrees), starts at maximum
value (1), crosses the x axis at 90+180n
Know how to graph a tangent
function.
x
Periodic (180 degrees), asymptotes
whenever cos = 0, shaped like a cubic
function
Understand what it means to be a
periodic function.
x
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.
x
tan x = sin x / cos x
Know the sign of sine, cosine and
tangent in each quadrant.
x
Understands how to use inverse
trigonometric functions to find the
value of needed.
x
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.
x
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.
x
Find the reference angle, determine the
quadrant that has the correct sign
x
sin^2 + cos^2 = 1
Knows the complementary Identities
and can reason logically to prove.
x
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.
x
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.
x
sin (-x) = -sin x
cos (-x) = cos x
tan (-x) = -tan x
Knows the exact value of angles from
0 to 360.
x
Know the sin of a sum or difference
And can use it to find exact values of
angles.
x
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.
x
Cos (A+B) = cosAcosB - sinAsinB
Cos (A-B) = cosAcosB + sinAsinB