R Y G Explanation and/or definition
Ch 8 Concept Workshop
Know the basics of right triangle trigonometry
Extending the Sine and cosine functions to all angles
Know how to graph a sine function.
Know how to graph a cosine function. x S-O-H C-A-H T-O-A x An angles’ intersection with the unit circle
(Sin: y value, cos: x value) x Periodic (360 degrees), starts at 0, crosses the origin, crosses the x axis at 180n 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.
Know the sign of sine, cosine and tangent in each quadrant.
Understands how to use inverse trigonometric functions to find the value of needed.
Can use a reference angle to find the value of a given angle. x tan x = sin x / cos x x Q1 - all (sin +, cos +, tan +)
Q2 - students (sin +, cos -, tan -)
Q3 - take (sin -, cos -, tan +)
Q4 - calculus (sin -, cos +, tan -) x 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 #) 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.
Knows the opposite angle Identities and can reason logically to prove.
Knows the exact value of angles from
0 to 360.
Know the sin of a sum or difference
And can use it to find exact values of angles.
Know the cosine of a sum or difference. x sin (180-x) = sin x cos (180-x) = -cos x
(tan (180-x) = -tan x) x sin (-x) = -sin x cos (-x) = cos x tan (-x) = -tan x x θ
0
30
45
60
90
180
270
360
Cos
θ
Sin
θ
Tan
θ x sin (A+B) = sinAcosB + sinBcosA sin (A-B) = sinAcosB - sinBcosA x Cos (A+B) = cosAcosB - sinAsinB
Cos (A-B) = cosAcosB + sinAsinB