Consider the arc of length s on the unit circle that begins at the point (1, 0) and ends at the point (−0.4898, −0.7864). Find csc s, sec s, cot s.

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In general the coordinates of a point P on a unit circle are given by

( cos θ. sin θ) where θ is the angle at the center from (1, 0) to the point P measured in radians (anticlockwise)

Since the point P is (−0.4898, −0.7864)

we conclude that cos θ. = −0.4898 and sin θ = −0.7864

From these, we can find the other ratios:

csc θ = 1/sin θ

= 1/−0.7864

= -1.2716

sec θ = 1/cos θ

= 1/−0.4898

=-2.0146

and cot θ = cos θ/sin θ

= −0.4898/ −0.7864

= 0.6228

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