Trigonometry Equations Part III

Trig Identities, Formulas, Graphing, and Inverse Functions

51 cards | Total Attempts: 188 | Created by Grendll | Last updated: Sep 18, 2015 | Total Attempts: 188

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Graph One Complete Cycle Of 4(cos 2x - π /2)

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Cards In This Set

Front	Back
Graph one complete cycle of 4(cos 2x - π /2)
Find the equation to match:	y = 4cos πx
Verify product formula 3 for A = 30 degrees and B = 120 degrees	Veriry Product Formula 3Substitute A = 30 degrees and B = 120 degrees into cosAcosB = 1/2[cos (A+B) + cos (A-B)]cos 30° cos120° = 1/2[cos150° + cos(-90° )]= √3/2(-1/2) = 1/2(- √3/2 +0) - √3/4 = √3/4 True statement.
Write 10cos 5xsin as sum or difference	Product Formula 2 is appropriate for an expression of the form cosA sinB. If we subsititute A = 5x and B = 3x:10 cos 5x sin 3x = 10 • 1/2[sin(5x + 3x) - sin(5x-3x)]= 5(sin 9x - sin 2x)
Write out the Sum and Difference Formulas (there are 6)
Write out the Double Angle Formulas(there are 5)
Proving Identities:Prove that tan x + cos x = sin x (sec x + cot x)	Sin x (sec x + cot x)= sin x sec x + sin x cot x= sinx • 1/ cos x + sin x • cos x/sin x= sin x/cos x + cos x= tan x + cos x
Find the exact value for cos 75°	= cos(45° + 30°= cos 45° cos 30°= - sin 45° sin 30°= $= cos(45° + 30°= cos 45° cos 30°= - sin 45° sin 30°= 2/2 • 3/2 - 2/2 • 1/2= 6 - 2 all over 4$ 2/2 • $= cos(45° + 30°= cos 45° cos 30°= - sin 45° sin 30°= 2/2 • 3/2 - 2/2 • 1/2= 6 - 2 all over 4$ 3/2 - $= cos(45° + 30°= cos 45° cos 30°= - sin 45° sin 30°= 2/2 • 3/2 - 2/2 • 1/2= 6 - 2 all over 4$ 2/2 • 1/2= $= cos(45° + 30°= cos 45° cos 30°= - sin 45° sin 30°= 2/2 • 3/2 - 2/2 • 1/2= 6 - 2 all over 4$ 6 - $= cos(45° + 30°= cos 45° cos 30°= - sin 45° sin 30°= 2/2 • 3/2 - 2/2 • 1/2= 6 - 2 all over 4$ 2 all over 4
Express sin13°cos48° as a sum.	SinAcosB = 1/2[sin(A + B) + sin(A - B)] sin13°cos48° = 1/2[sin(13° + 48°) + sin(13° - 48°)] Perform the operations and simplify. = 1/2(sin61° + sin(-35°) Remember that sine is an odd function. Answer: sin13°cos48° = 1/2(sin61° - sin35°)
Sin75° = sin(45° + 30°)	( $(6 +2)/4 sin75° = sin(45° + 30°) sin(A + B) = sinAcosB + cosAsinB Sum and Difference Formula. sin(45° + 30°) = sin45°cos30° + cos45°sin30° = (2/2)(£3/2) + (2/2)(1/2) Obtain these values from the Unit Circle. = 6/4 + 2/4 Perform the operations. = (6 + 2)/4 Simplify.$ 6 + $(6 +2)/4 sin75° = sin(45° + 30°) sin(A + B) = sinAcosB + cosAsinB Sum and Difference Formula. sin(45° + 30°) = sin45°cos30° + cos45°sin30° = (2/2)(£3/2) + (2/2)(1/2) Obtain these values from the Unit Circle. = 6/4 + 2/4 Perform the operations. = (6 + 2)/4 Simplify.$ 2)/4 sin75° = sin(45° + 30°) sin(A + B) = sinAcosB + cosAsinB Sum and Difference Formula. sin(45° + 30°) = sin45°cos30° + cos45°sin30° = ( $(6 +2)/4 sin75° = sin(45° + 30°) sin(A + B) = sinAcosB + cosAsinB Sum and Difference Formula. sin(45° + 30°) = sin45°cos30° + cos45°sin30° = (2/2)(£3/2) + (2/2)(1/2) Obtain these values from the Unit Circle. = 6/4 + 2/4 Perform the operations. = (6 + 2)/4 Simplify.$ 2/2)(£3/2) + ( $(6 +2)/4 sin75° = sin(45° + 30°) sin(A + B) = sinAcosB + cosAsinB Sum and Difference Formula. sin(45° + 30°) = sin45°cos30° + cos45°sin30° = (2/2)(£3/2) + (2/2)(1/2) Obtain these values from the Unit Circle. = 6/4 + 2/4 Perform the operations. = (6 + 2)/4 Simplify.$ 2/2)(1/2) Obtain these values from the Unit Circle. = $(6 +2)/4 sin75° = sin(45° + 30°) sin(A + B) = sinAcosB + cosAsinB Sum and Difference Formula. sin(45° + 30°) = sin45°cos30° + cos45°sin30° = (2/2)(£3/2) + (2/2)(1/2) Obtain these values from the Unit Circle. = 6/4 + 2/4 Perform the operations. = (6 + 2)/4 Simplify.$ 6/4 + $(6 +2)/4 sin75° = sin(45° + 30°) sin(A + B) = sinAcosB + cosAsinB Sum and Difference Formula. sin(45° + 30°) = sin45°cos30° + cos45°sin30° = (2/2)(£3/2) + (2/2)(1/2) Obtain these values from the Unit Circle. = 6/4 + 2/4 Perform the operations. = (6 + 2)/4 Simplify.$ 2/4 Perform the operations. = ( $(6 +2)/4 sin75° = sin(45° + 30°) sin(A + B) = sinAcosB + cosAsinB Sum and Difference Formula. sin(45° + 30°) = sin45°cos30° + cos45°sin30° = (2/2)(£3/2) + (2/2)(1/2) Obtain these values from the Unit Circle. = 6/4 + 2/4 Perform the operations. = (6 + 2)/4 Simplify.$ 6 + $(6 +2)/4 sin75° = sin(45° + 30°) sin(A + B) = sinAcosB + cosAsinB Sum and Difference Formula. sin(45° + 30°) = sin45°cos30° + cos45°sin30° = (2/2)(£3/2) + (2/2)(1/2) Obtain these values from the Unit Circle. = 6/4 + 2/4 Perform the operations. = (6 + 2)/4 Simplify.$ 2)/4 Simplify.
cos135° = cos(90° + 45°)	Answer: 0 cos2A, A = pi/4 cos2A = cos^2 A - sin^2 A Half Angle Formulae cos2(pi/4) = cos^2 pi/4 - sin^2 pi/4 = ( $Answer: 0 cos2A, A = pi/4 cos2A = cos^2 A - sin^2 A Half Angle Formulae cos2(pi/4) = cos^2 pi/4 - sin^2 pi/4 = (2/2)^2 - (2/2)^2 Obtain these values from the Unit Circle. = 0 Perform the operations.$ 2/2)^2 - ( $Answer: 0 cos2A, A = pi/4 cos2A = cos^2 A - sin^2 A Half Angle Formulae cos2(pi/4) = cos^2 pi/4 - sin^2 pi/4 = (2/2)^2 - (2/2)^2 Obtain these values from the Unit Circle. = 0 Perform the operations.$ 2/2)^2 Obtain these values from the Unit Circle. = 0 Perform the operations.
Tan195° = tan(225° - 30°)	Answer: - $Answer: -3 tan2A, tan = 60° tan2A = (2tanA)/(1 - tan^2 A) Half Angle Formulae. tan2(60°) = (2tan60°)/(1 - tan^2 60°) = 2(3)/(1 - (3)^2) Obtain these values from the Unit Circle. = 23/(1 - 3) = 23/-2 = -3 Perform the operations and simplify.$ 3 tan2A, tan = 60° tan2A = (2tanA)/(1 - tan^2 A) Half Angle Formulae. tan2(60°) = (2tan60°)/(1 - tan^2 60°) = 2( $Answer: -3 tan2A, tan = 60° tan2A = (2tanA)/(1 - tan^2 A) Half Angle Formulae. tan2(60°) = (2tan60°)/(1 - tan^2 60°) = 2(3)/(1 - (3)^2) Obtain these values from the Unit Circle. = 23/(1 - 3) = 23/-2 = -3 Perform the operations and simplify.$ 3)/(1 - ( $Answer: -3 tan2A, tan = 60° tan2A = (2tanA)/(1 - tan^2 A) Half Angle Formulae. tan2(60°) = (2tan60°)/(1 - tan^2 60°) = 2(3)/(1 - (3)^2) Obtain these values from the Unit Circle. = 23/(1 - 3) = 23/-2 = -3 Perform the operations and simplify.$ 3)^2) Obtain these values from the Unit Circle. = 2 $Answer: -3 tan2A, tan = 60° tan2A = (2tanA)/(1 - tan^2 A) Half Angle Formulae. tan2(60°) = (2tan60°)/(1 - tan^2 60°) = 2(3)/(1 - (3)^2) Obtain these values from the Unit Circle. = 23/(1 - 3) = 23/-2 = -3 Perform the operations and simplify.$ 3/(1 - 3) = 2 $Answer: -3 tan2A, tan = 60° tan2A = (2tanA)/(1 - tan^2 A) Half Angle Formulae. tan2(60°) = (2tan60°)/(1 - tan^2 60°) = 2(3)/(1 - (3)^2) Obtain these values from the Unit Circle. = 23/(1 - 3) = 23/-2 = -3 Perform the operations and simplify.$ 3/-2 = - $Answer: -3 tan2A, tan = 60° tan2A = (2tanA)/(1 - tan^2 A) Half Angle Formulae. tan2(60°) = (2tan60°)/(1 - tan^2 60°) = 2(3)/(1 - (3)^2) Obtain these values from the Unit Circle. = 23/(1 - 3) = 23/-2 = -3 Perform the operations and simplify.$ 3 Perform the operations and simplify.
Use the double angle formulae for the given values. cos2A, A = pi/4	Answer: 0 cos2A, A = pi/4 cos2A = cos^2 A - sin^2 A Half Angle Formulae cos2(pi/4) = cos^2 pi/4 - sin^2 pi/4 = ( $Answer: 0 cos2A, A = pi/4 cos2A = cos^2 A - sin^2 A Half Angle Formulae cos2(pi/4) = cos^2 pi/4 - sin^2 pi/4 = (2/2)^2 - (2/2)^2 Obtain these values from the Unit Circle. = 0 Perform the operations.$ 2/2)^2 - ( $Answer: 0 cos2A, A = pi/4 cos2A = cos^2 A - sin^2 A Half Angle Formulae cos2(pi/4) = cos^2 pi/4 - sin^2 pi/4 = (2/2)^2 - (2/2)^2 Obtain these values from the Unit Circle. = 0 Perform the operations.$ 2/2)^2 Obtain these values from the Unit Circle. = 0 Perform the operations.
Use the double angle formulae for the given values.tan2A, A = 60°	Answer: - $Answer: -3 tan2A, tan = 60° tan2A = (2tanA)/(1 - tan^2 A) Half Angle Formulae. tan2(60°) = (2tan60°)/(1 - tan^2 60°) = 2(3)/(1 - (3)^2) Obtain these values from the Unit Circle. = 23/(1 - 3) = 23/-2 = -3 Perform the operations and simplify.$ 3 tan2A, tan = 60° tan2A = (2tanA)/(1 - tan^2 A) Half Angle Formulae. tan2(60°) = (2tan60°)/(1 - tan^2 60°) = 2( $Answer: -3 tan2A, tan = 60° tan2A = (2tanA)/(1 - tan^2 A) Half Angle Formulae. tan2(60°) = (2tan60°)/(1 - tan^2 60°) = 2(3)/(1 - (3)^2) Obtain these values from the Unit Circle. = 23/(1 - 3) = 23/-2 = -3 Perform the operations and simplify.$ 3)/(1 - ( $Answer: -3 tan2A, tan = 60° tan2A = (2tanA)/(1 - tan^2 A) Half Angle Formulae. tan2(60°) = (2tan60°)/(1 - tan^2 60°) = 2(3)/(1 - (3)^2) Obtain these values from the Unit Circle. = 23/(1 - 3) = 23/-2 = -3 Perform the operations and simplify.$ 3)^2) Obtain these values from the Unit Circle. = 2 $Answer: -3 tan2A, tan = 60° tan2A = (2tanA)/(1 - tan^2 A) Half Angle Formulae. tan2(60°) = (2tan60°)/(1 - tan^2 60°) = 2(3)/(1 - (3)^2) Obtain these values from the Unit Circle. = 23/(1 - 3) = 23/-2 = -3 Perform the operations and simplify.$ 3/(1 - 3) = 2 $Answer: -3 tan2A, tan = 60° tan2A = (2tanA)/(1 - tan^2 A) Half Angle Formulae. tan2(60°) = (2tan60°)/(1 - tan^2 60°) = 2(3)/(1 - (3)^2) Obtain these values from the Unit Circle. = 23/(1 - 3) = 23/-2 = -3 Perform the operations and simplify.$ 3/-2 = - $Answer: -3 tan2A, tan = 60° tan2A = (2tanA)/(1 - tan^2 A) Half Angle Formulae. tan2(60°) = (2tan60°)/(1 - tan^2 60°) = 2(3)/(1 - (3)^2) Obtain these values from the Unit Circle. = 23/(1 - 3) = 23/-2 = -3 Perform the operations and simplify.$ 3 Perform the operations and simplify.
Verify the identity: tan2x = (2tan x)/(1 - tan^2 x)	Tan2x = tan(x + x) Split the angle. = (tanx + tanx)/(1 - tan x tan x) Use the Sum and Difference Formulae. = (2tanx)/(1 - tan^2 x) Simplify.