alleryStart learning →What do the reduction formulas accomplish?
AThey raise the power of a trigonometric term by one
BThey reduce the power of a trigonometric term
CThey convert a product into a sum of two terms
DThey convert an angle into its complement angle
Answer & Solution
Correct answer: B. They reduce the power of a trigonometric term
1. The reduction formulas are derived from the double-angle formulas for cosine.
2. They rewrite an even power of sine or cosine using the first power of a cosine at a doubled angle.
3. For example sin^2 x becomes (1 - cos(2x)) / 2, so the exponent drops from two to one.
4. Turning products into sums is the job of the product-to-sum formulas, a separate family.
_Source: OpenStax Algebra and Trigonometry (CC BY 4.0), Ch 9 "Trigonometric Identities and Equations", section 9.3 Double-Angle, Half-Angle, and Reduction Formulas_
Keep practising Trigonometric Identities and Equations
Browse all Trigonometric Identities and Equations questions for B.Sc Mathematics, or explore more Mathematics topics.
Related questions
If a ladder's base is a feet from the wall and its length is 4a feet, how high up the wallSafety rules place a ladder's base 1 foot from the wall for every 4 feet of ladder length.Compared with y = sin t, the graph of y = sin(2t) is which transformation?Solving sin(n t) = c across one turn requires going around the unit circle how many times?Solve cos(2t) = 1/2 on the interval from 0 to 2 pi.Solve 3 cos t + 3 = 2 sin^2 t exactly on the interval from 0 to 2 pi.Solve cos t cos(2t) + sin t sin(2t) = sqrt(3)/2 on the interval from 0 to 2 pi.Solve 2 sin^2 t + sin t = 0 exactly on the interval from 0 to 2 pi.