Find a trigonometric equation describing a given solution set Write a trigonometric equation whose solution is the set given: {x|x=pi/8+pi/(2k)vv x=(-pi)/8+pi/(2k), k in Z}

Howard Nelson

Howard Nelson

Answered question

2022-11-02

Find a trigonometric equation describing a given solution set
Write a trigonometric equation whose solution is the set given: Β  { π‘₯ | π‘₯ = Ο€ 8 + Ο€ 2 π‘˜ Β  ∨ Β  π‘₯ = βˆ’ Ο€ 8 + Ο€ 2 π‘˜ , π‘˜ ∈ 𝒁 }
From what is provided in the equation, Ο€ / 2 k is the period and it is possibly tangent. I am having trouble figuring out where to go next.
I have tried:
graphing it on desmos to see if fiddling with it will magically show the equation.
graphed it on a unit circle and I have found that it is possibly a tangent equation based on the +/- Ο€ / 8. It is in the first and fourth quadrant, therefore its tangent.
tried solving with the half-angle formula for tangent, but I get stuck figuring out where to input the what in the equation. I also don't know how to get cosine.

Answer & Explanation

brulotfao

brulotfao

Beginner2022-11-03Added 16 answers

you have
x = Β± Ο€ 8 + Ο€ 2 k
This can be rearranged as
Ο€ 2 x βˆ“ Ο€ 8 = 2 k Ο€
So one possible trig equation could be
sin ⁑ ( Ο€ 2 x βˆ“ Ο€ 8 ) = 0

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