Transformation Formulae
Math ⇒ Trigonometry
Transformation Formulae starts at 11 and continues till grade 12.
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See sample questions for grade 11
Explain the difference between sum-to-product and product-to-sum formulae in trigonometry.
Express cos(15°) in terms of cos(45°) and cos(30°) using the difference formula.
Express cos(75°) in terms of cos(45°) and cos(30°) using the appropriate transformation formula.
Express sin(75°) in terms of sin(45°) and cos(30°) using the sum formula.
If cosA = 0.8 and sinA = 0.6, find cos(2A).
If sinA = 0.5 and cosB = 0.5, find sinA cosB using the product-to-sum formula.
If sinA = 0.6 and sinB = 0.8, find sinA + sinB using the sum-to-product formula.
If sinA = 3/5 and cosB = 4/5, find sin(A + B) given that both A and B are in the first quadrant.
Which of the following is the correct formula for cosA - cosB?
(1) -2 sin[(A + B)/2] sin[(A - B)/2]
(2) 2 sin[(A + B)/2] sin[(A - B)/2]
(3) 2 cos[(A + B)/2] cos[(A - B)/2]
(4) -2 cos[(A + B)/2] cos[(A - B)/2]
Which of the following is the correct formula for cosA sinB?
(1) 1/2 [sin(A + B) + sin(A - B)]
(2) 1/2 [sin(A + B) - sin(A - B)]
(3) 1/2 [cos(A + B) + cos(A - B)]
(4) 1/2 [cos(A + B) - cos(A - B)]
Which of the following is the correct formula for sin(2A)?
(1) 2sinA cosA
(2) sin²A + cos²A
(3) 2cosA
(4) sinA + cosA
Which of the following is the correct formula for sin(A)sin(B)?
(1) 1/2 [cos(A - B) - cos(A + B)]
(2) 1/2 [sin(A + B) + sin(A - B)]
(3) 1/2 [cos(A + B) + cos(A - B)]
(4) 1/2 [sin(A + B) - sin(A - B)]
Fill in the blank: cos(2A) = 1 - 2 ________.
Fill in the blank: cosA + cosB = 2 cos[(A + B)/2] ________.
Fill in the blank: cosA cosB = 1/2 [__________].
Fill in the blank: sin(A + B) = _________.
True or False: cos(2A) = 2cos²A - 1.
True or False: cosA - cosB = -2 sin[(A + B)/2] sin[(A - B)/2].
True or False: cosA + cosB = 2 cos[(A + B)/2] cos[(A - B)/2].
True or False: cosA cosB = 1/2 [cos(A + B) + cos(A - B)].
