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MATH / There exist constants a, b, c, and d such that

Problem

Answer published by the source. Consult the official source to check your work against its answer.

problem

There exist constants aa, bb, cc, and dd such that (sinx)7=asin7x+bsin5x+csin3x+dsinx(\sin x)^7 = a \sin 7x + b \sin 5x + c \sin 3x + d \sin xfor all angles xx. Find dd.
Plain-text mathematical notation (without MathML)
There exist constants a, b, c, and d such that
(sinx)⁷=asin7x+bsin5x+csin3x+dsinxfor all angles x.  Find d.
Original LaTeX notation
There exist constants $a$, $b$, $c$, and $d$ such that
\[(\sin x)^7 = a \sin 7x + b \sin 5x + c \sin 3x + d \sin x\]for all angles $x$.  Find $d$.

level

Level 4

type

Precalculus

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Source and history

task_id
3480164f-84a6-5d38-8428-7490e4c1a388
task_key
precalculus--test--3480164f-84a6-5d38-8428-7490e4c1a388
task_revision_id
1
config / split
precalculus / test

Official source

initial import