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Math Help - Finding trig functions given constraints

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    Senior Member vaironxxrd's Avatar
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    Finding trig functions given constraints

    A function value is given along with constraints and I must find all other trig functions based on the given values.

    Function value: tan \theta is undefined
    Constraints: \pi \le \theta \le 2\pi

    I can't completely figure out the solution but I've done some work "trying".
    First..
    tan \theta = \frac{o}{a} = \frac{y}{x} meaning that x is equal to 0. because of the constraints I made an unit circle and assumed theta is \frac{3\pi}{2}
    Therefore,

    sin \theta = ?
    cos\theta = ?
    tan\theta = undefined
    csc\theta = ?
    sec\theta = undefined
    cot\theta = ?

    Am I on the right track? Could anyone also point me in the right direction?
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    Re: Finding trig functions given constraints

    Hey vaironxxrd.

    Are you just trying to find when the trig functions are undefined? If so then use the fact that tan(theta) = sin(theta)/cos(theta) and put all trig functions into rational functions (like I did with tan) and find when the denominator is equal to 0 (which will mean its undefined there).
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    Senior Member vaironxxrd's Avatar
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    Re: Finding trig functions given constraints

    Quote Originally Posted by chiro View Post
    Hey vaironxxrd.

    Are you just trying to find when the trig functions are undefined? If so then use the fact that tan(theta) = sin(theta)/cos(theta) and put all trig functions into rational functions (like I did with tan) and find when the denominator is equal to 0 (which will mean its undefined there).
    Thank you for the advice Chiro. The question is asking me to find the values of all six trig functions, I assume I must use tan for that (as you said).
    I'm just confused if I must make an unit circle and used the x,y,r values or just use an angle value. I feel the question doesn't give enough information for the x,y,r.
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    Re: Finding trig functions given constraints

    One suggestion I have is use the fact for a circle, x = rcos(t) and y = rsin(t) for a circle of radius r centered at the origin. Once you solve for t in radians you can plug in the value to get the (x,y) point.
    Thanks from topsquark
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    Senior Member vaironxxrd's Avatar
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    Re: Finding trig functions given constraints

    Quote Originally Posted by chiro View Post
    One suggestion I have is use the fact for a circle, x = rcos(t) and y = rsin(t) for a circle of radius r centered at the origin. Once you solve for t in radians you can plug in the value to get the (x,y) point.
    I was able to figure out a method for solving it, hopefully you can correct me on a more efficient way.

    Because tan Θ is undefined and the constraints say it must lie between Quadrant 3 or 4, I was able to figure out that theta must be 3pi/2.
    The reason is because at angle 3pi/2 x = 0 and therefore making tan \theta = \frac{opp}{adj} = \frac{y}{x} undefined.
    x = 0 and y = -1 .
    I then proceded to solve the functions

    sin = \frac{opp}{hyp} = \frac{y}{r} = -1
    cos = \frac{adj}{hyp} = \frac{x}{r} = 0
    tan = \frac{opp}{adj} = \frac{y}{x} = Undefined
    csc = \frac{hyp}{opp} = \frac{r}{y} = -1
    sec = \frac{hyp}{adj} = \frac{r}{x} = Undefined
    cot = \frac{adj}{opp} = \frac{x}{y} = 0

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    Re: Finding trig functions given constraints

    Looks pretty good.
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