Find the values of the trigonometric function cot -8/17

sin:
sec:
tan:
cot:

I know you use a Pythagorean Identity, sin^2t + cos^2t=1

I got 64/289 for the first one for example and it was wrong.

1 answer

  1. Your terminology is awful

    cot - 8/17 is meaningless

    I will assume you were given cot Ø = -8/17 and are asked to find the remaining 5 trig ratios

    if cot Ø = -8/17, then tan Ø = -17/8

    you should also have memorized the 3 main trig functions in terms of x, y, and r
    e.g. tan Ø = y/x = -17/8 ---> terminal point (8, -17)
    or
    tan Ø = y/x = 17/-8 ----> terminal point (-8,17)


    From the CAST rule we know that Ø must be either in quadrants II or IV , as seen from the position of the terminal arm points.
    so make appropriate sketches showing right-angled triangles .

    x^2 + y^2 = r^2 , taking one of the points
    r^2 = 8^2 + (-17)^2
    r^2 = 353
    r = √353 , (r is always positive)

    sinØ = y/r = 17/√353 or sinØ = 17/√353
    cosØ = ±8/√353 so
    secØ = ± √353/8
    etc using the basic definitions.

    Let me know if my assumption was not correct

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