i understand how sine cos and tan are positive in their respective quadrants, but how is sine in quad 1 and quad 2 the same value, and tan 360-theta and tan theta the same value, etc? how do we know and show proof?
In: 1
Their values are illustrated by the unit circle, as shown [here](https://www.mathsisfun.com/algebra/trig-interactive-unit-circle.html).
Beginning at the upper left going anti-clockwise, quadrants are numbered 1, 2, 3, and 4.
𝛉 equals 0° for a line that intercepts the circle at the positive side of the X axis.
Sine describes the distance from the X axis of the point where 𝛉 intercepts the unit circle. If this point lies above the X axis, then sine is positive. If it lies below the X axis, then it is negative.
Cosine is like sine, but uses the Y axis and is always 90 degrees out of phase from sine, hence is its “co”-sine.
Tangent describes the length of a line that extends *from* the X axis to the point where it is tangent to the unit circle at 𝛉. So if the tangent line extends up from the X axis, it is positive; if it extends down, it is negative.
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