What quadrant(s) that all functions are negative in the unit circle? Is it even possible?

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What quadrant(s) that all functions are negative in the unit circle? Is it even possible?

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Answer 1 · 2018-07-11T19:34:45

Having each function negative in the unit circle is not possible.

Explanation:

In the unit circle the quadrants have the following signs.
Quadrant I $(+, +)$ $(+,+)$
Quadrant II $(-, +)$ $(-,+)$
Quadrant III $(-, -)$ $(-,-)$
Quadrant IV $(+, -)$ $(+,-)$

Where #(x,y) are the coordinates of the graph.

For the trigonometric functions

Cosine - $cos = x$ $cos = x$

Sine - $sin = y$ $sin = y$
Secant - $sec = \frac{1}{x}$ $sec = 1/x$
Cosecant - $csc = \frac{1}{y}$ $csc = 1/y$
Tangent - $tan = \frac{y}{x}$ $tan =y/x$
Cotangent - $c t n = \frac{x}{y}$ $ctn = x/y$

The six functions have the following signs in each quadrant:

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What quadrant(s) that all functions are negative in the unit circle? Is it even possible?

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Explanation:

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