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Trigonometric Equations

Equations with trigonometry in them can look scary, but that's nothing that a quick little substitution can't fix.

Specific Solution

         

How many solutions are there to \( \sin \theta + 7 = 8 \) in the domain \( [0 ^ \circ, 1000 ^ \circ ] \)?

What is the minimum value of a positive number \(x\) such that the value of \(\sin(x+\frac{\pi}{8})\) is \(0?\)

How many \(x\)'s in the interval \(0 \leq x \leq 15\pi\) satisfy \(\tan x=-\sqrt{3}\)?

What are the solutions to \(12\sin \left( 2x-\frac{7}{6}\pi \right)=6\sqrt{2}\) in the interval \(x \in [0,\pi]?\)

Which of the following is a solution to

\[ \sin ( 2 \theta - 31 ^ \circ ) = \cos 49 ^ \circ ? \]

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