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Transformation Formulae

Math ⇒ Trigonometry

Transformation Formulae starts at 11 and continues till grade 12. QuestionsToday has an evolving set of questions to continuously challenge students so that their knowledge grows in Transformation Formulae. How you perform is determined by your score and the time you take. When you play a quiz, your answers are evaluated in concept instead of actual words and definitions used.
See sample questions for grade 12
Describe the importance of transformation formulae in solving trigonometric equations.
Explain how transformation formulae can be used to simplify the expression sinx + sin3x.
Express cosA - cosB as a product of sines.
Express cosA + cosB as a product.
Explain how transformation formulae can be used to simplify the expression sinx + sin3x.
If A = 75° and B = 15°, calculate sinA + sinB using the sum-to-product formula.
If cosA + cosB = 2 cos[(A+B)/2] cos[(A-B)/2], what is cos120° + cos60°?
If cosA = 0.6 and cosB = 0.8, find cosA cosB using the product-to-sum formula.
Which of the following is NOT a transformation formula? (1) sinA + sinB = 2 sin[(A+B)/2] cos[(A-B)/2] (2) cosA cosB = 1/2 [cos(A+B) + cos(A-B)] (3) tanA + tanB = sin(A+B)/cosA cosB (4) sinA sinB = 1/2 [cos(A-B) - cos(A+B)]
Which of the following is the correct formula for cosA - cosB? (1) 2 sin[(A+B)/2] sin[(A-B)/2] (2) 2 cos[(A+B)/2] cos[(A-B)/2] (3) -2 sin[(A+B)/2] sin[(A-B)/2] (4) 2 sin[(A-B)/2] cos[(A+B)/2]
Which of the following is the correct formula for cosA cosB? (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)]
Which of the following is the correct formula for sinA cosB? (1) 1/2 [sin(A+B) + sin(A-B)] (2) 1/2 [cos(A+B) + cos(A-B)] (3) 1/2 [sin(A+B) - sin(A-B)] (4) 1/2 [cos(A+B) - cos(A-B)]
Fill in the blank: cos(A + B) = _________.
Fill in the blank: cosA + cosB = 2 cos[(A+B)/2] ________.
Fill in the blank: sinA - sinB = 2 cos[(A+B)/2] ________.
Fill in the blank: sinA cosB = 1/2 [______ + sin(A-B)].
True or False: cosA cosB = 1/2 [cos(A+B) + cos(A-B)]
True or False: sin(A + B) = sinA + sinB.
True or False: The formula sinA cosB = 1/2 [sin(A+B) + sin(A-B)] can be used to express the product of sine and cosine as a sum.
True or False: The sum-to-product and product-to-sum formulae are collectively called transformation formulae.