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Graphs of Trigonometric Functions

Plot the six different trig functions, discover their illuminating interactions, and ride the wave!

Symmetry

         

Given that \( \sin 41 ^ \circ = \cos N ^ \circ \), where \( 0 \leq N \leq 90 \), what is the value of \(N\)?

If \(\sin\theta=\frac{\sqrt{5}}{5}\) and \(\frac{\pi}{2}<\theta<\pi,\) what is the value of \(\cos(-\theta)?\)

Let \(f(x)=\sin x\) and \(g(x)=\tan x.\) If \(g(f(\theta))\)=\(\frac{\sqrt{3}}{7}\), what is the value of \(g(f(-\theta))?\)

If \(\tan\theta=15,\) what is the value of \(-\tan(-\theta)?\)

If \(\cos\theta=\frac{\sqrt{7}}{5}\) and \(0<\theta<\frac{\pi}{2},\) what is the value of \(\tan(-\theta)?\)

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