please explain me the quadrant cycle of trigonometry..... please don't spam... answer fast!
Answers
Answer:
The coordinate axes divide the plane into four quadrants, labelled first, second, third and fourth as shown. ... 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.
Answer:
Quadrant rule of trigonometry
In the first quadrant, the values for sin, cos and tan are positive. ... In the fourth quadrant, the values for cos are positive only. This can be summed up as follows: In the fourth quadrant, Cos is positive, in the first, All are positive, in the second, Sin is positive and in the third quadrant, Tan is positive.
Step-by-step explanation:
The four quadrants
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∘.
Illustration of coordinate axes with quadrants labelled one, two, three, four.
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.
Two illustrations of coordinate axes. Four quadrants identified with the sign of each of the trigonometric ratios in a given quadrant.
Detailed description of diagram
Related angles
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 (cos 210∘,sin 210∘). The angle POQ is 30∘ and is called the related angle for 210∘.
Circle with radius of 1, centre of circle at origin O. Point marked on circle in quadrant 1 as (cos 30 degrees, sin 30 degrees).