Trig equations (1 Viewer)

kpad5991 · Jan 27, 2018

Solve

2 cos x = 1-1/2x

HeroWise · Jan 27, 2018

What do they want you to solve for ?

Cant you just make x the subject? please elaborate a bit more so we can help you

kpad5991 · Jan 27, 2018

It's says prove algebraically that if n is a solution of the equation in part c (which is the above equation) then n is greater than and equal to -2 but less than and equal 6

fan96 · Jan 28, 2018

The wording hints that you're expected to provide an answer without solving the equation. Solving the equation seems rather hard. I can't think of any ways to express $\cos x$ in terms of $x$ without losing the $x$ on the RHS. Wolfram Alpha also has trouble providing exact answers to it.

Although the question asks for an algebraic proof, visualising the problem with a graph really helps in understanding it and devising a solution.

$2 \cos x = 1 - \frac{1}{2}x$

$4 \cos x = 2 - x$

Clearly $-4 \leq 4 \cos x \leq 4$ , therefore:

$\begin{aligned} -4 &\leq 2 - x \leq 4 \\ -6 &\leq -x \leq 2 \\ 6 &\geq x \geq -2\end{aligned}$

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Trig equations (1 Viewer)

kpad5991

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kpad5991

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fan96

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