- #1

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[tex] \sin \theta = \cos \theta [/tex]

\theta=\frac{\pi}{4}

2.

[tex] \sin \theta = \tan \theta [/tex]

[tex]\theta = 0[/tex]

3.

[tex] \cos \theta = \tan \theta [/tex]

[tex] \theta =\arcsin (\varphi -1) [/tex]

4.

[tex]\sin \theta = \csc \theta[/tex]

[tex]\theta = \frac{\pi}{2}[/tex]

5.

[tex]\sin \theta =\sec \theta[/tex]

[tex]\theta[/tex] does not exist.

6.

[tex]\sin \theta =\cot \theta[/tex]

[tex]\theta = \arccos (\varphi -1)[/tex]

7.

[tex]\cos \theta =\csc \theta[/tex]

[tex]\theta[/tex] does not exist.

8.

[tex]\cos \theta =\sec \theta[/tex]

[tex]\theta=0[/tex]

9.

[tex]\cos \theta = \cot \theta [/tex]

[tex]\theta=\frac{\pi}{2}[/tex]

10.

[tex]\tan \theta =\csc \theta[/tex]

[tex]\theta =\arccos(\varphi-1)[/tex]

11.

[tex]\tan \theta = \sec \theta [/tex]

[tex]\theta=\frac{\pi}{2}[/tex]

12.

[tex]\tan \theta = \cot \theta [/tex]

[tex]\theta=\frac{\pi}{4}[/tex]

13.

[tex]\csc \theta =\sec \theta[/tex]

[tex]\theta=\frac{\pi}{4}[/tex]

14.

[tex]\csc \theta =\cot \theta [/tex]

[tex]\theta = \arccos (\varphi -1) [/tex]

15.

[tex] \sec \theta =\cot \theta [/tex]

[tex]\theta=\arcsin (\varphi - 1) [/tex]

I used quadratic equation for some equalities. Which showed that the golden ration was involved. But my question is "geometrically, why?"