Trigonometry, a branch of mathematics, involves six primary functions: sine (sin), cosine (cos), tangent (tan), cosecant (cosec), secant (sec), and cotangent (cot). To determine the signs of these functions, we use a unit circle, a circle with a radius of one, centered at the origin of a coordinate system, as shown below:
For any point P (a, b) on the unit circle, both 'a' and 'b' values range between -1 and 1. Therefore, the values of cos x and sin x also lie between -1 and 1 for all x. Furthermore, we can assign different signs to 'a' and 'b' based on their quadrant:
First Quadrant: 0 < x < π/2, both 'a' and 'b' are positive.
Second Quadrant: π/2 < x < π, 'a' is negative and 'b' is positive.
Third Quadrant: π < x < 3π/2, both 'a' and 'b' are negative.
Fourth Quadrant: 3π/2 < x < 2π, 'a' is positive and 'b' is negative.
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