Geometry

# Symmetry in Trigonometric Graphs

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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