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Let X' OX and Y' OY be two lines at right angles to each other as in the figure. We call X' OX and Y' OY as X axis and Y axis respectively. Clearly these axes divided the entire plane into four equal parts called “Quadrants” .
The parts XOY, YOX' , X'OY' and Y'OX are known as the first, second, third and the fourth quadrant respectively.
In the first quadrant both x and y are positive. So all trigonometric ratios are positive. In the second quadrant (90° < θ <180°) x is negative and y is positive. So trigonometric ratios sin θ and cosec θ are positive. In the third quadrant (180° < θ < 270°) both x and y are negative. So trigonometric ratios tan θ and cot θ are positive. In the fourth quadrant (270° < θ < 360° ) x is positive and y is negative. So trigonometric ratios cos θ and sec θ are positive.
Two angles are said to be allied angles when their sum or difference is either zero or a multiple of 90° . The angles -θ , 90° ± θ, 180° ± θ,, 360° ± θ etc .,are angles allied to the angle θ. Using trigonometric ratios of the allied angles we can find the trigonometric ratios of any angle.
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