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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