Trigonometry · Intermediate · 7 min
Trigonometric equations
Solving a trigonometric equation means finding every angle in the stated domain.
WHAT HAPPENS IF…How many solutions does sinθ=1 have in [0,2π)?
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Let α=arcsin(c). The two solution families are α+2kπ and π−α+2kπ. Restrict them to the requested interval and remove duplicates. For |c|>1 there are no real solutions; this slider stays in [−1,1].
A detail that matters
A principal inverse value alone usually misses another solution.
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