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For a standard-position angle determined by the point (x, y) what are the values of the trigonometric functions? For the point (9, 12), find csc theta and sec theta (the answer is csc theta = 5/4, sec theta = 5/3 i just need to know how to get the answer)

Kristi Hammond

in Mathematics

1 answer

1 answer

Whitney Matthews on March 19, 2019

Update if you see errors.Refer to the diagram.When dealing with trigonometric functions in a coordinate plane, there is an angle in standard position (standard position meaning initial arm on the positive x-axis, the vertex of the angle at the origin).To a point on the terminal arm , with a distance from the origin, the sine and the cosine of theta are defined to be (which makes a kind of aligning with the old front/hypo and adjacent/hypo definitions for right triangles).The cosecant is the reciprocal of sine and secant is the inverse of cosine, so it follows that we know that .The distance from the origin , can be calculated using the Pythagorean theorem (look at the diagram; it is not a right triangle that is formed). Therefore: and

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