Angle θ lies in the second quadrant, and sin θ = .

The coordinate axes divide the plane into four quadrants, labelled first, second, third and fourth as shown. Angles in the third quadrant, for example, lie between 180∘ and 270∘ &By considering the x- and y-coordinates of the point P as it lies in each of the four quadrants, we can identify the sign of each of the trigonometric ratios in a given quadrant. These are summarised in the following diagrams.  &In the module Further trigonometry (Year 10), we saw that we could relate the sine and cosine of an angle in the second, third or fourth quadrant to that of a related angle in the first quadrant. The method is very similar to that outlined in the previous section for angles in the second quadrant.

We will find the trigonometric ratios for the angle 210∘, which lies in the third quadrant. In this quadrant, the sine and cosine ratios are negative and the tangent ratio is positive.

To find the sine and cosine of 210∘, we locate the corresponding point P in the third quadrant. The coordinates of P are (cos210∘,sin210∘). The angle POQ is 30∘ and is called the related angle for 210∘.

Step-by-step explanation:

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