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Math Help - I am having difficulty finding the exact values within a given interval

  1. #1
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    I am having difficulty finding the exact values within a given interval

    For some reason I am thrown off by trig questions asking to find the exact value(s) within a specified interval.

    Questions 1-2:

    Directions: Find the exact value of s:

    1. [0, pi / 2]; tan s = sqrt(3) / 3

    2. [-2pi, pi); tan^2 s = 3

    Question 3:

    Directions: Find all values of theta, if theta is in the interval [0 degrees, 360 degrees] and has the given function value:

    csc theta = sqrt(2)

    Could someone please provide direction as to how to solve these problems?
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  2. #2
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    Re: I am having difficulty finding the exact values within a given interval

    Hey Odonksy.

    There are some special values that have exact solutions.

    Hint: Look at the tangent of pi/3, pi/4, and pi/6.
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    Re: I am having difficulty finding the exact values within a given interval

    Quote Originally Posted by chiro View Post
    Hey Odonksy.

    There are some special values that have exact solutions.

    Hint: Look at the tangent of pi/3, pi/4, and pi/6.
    For Question 1, [0, pi / 2]; tan s = sqrt(3) / 3, I have determined that s equals pi/6 or 60 degrees, based on your hint.

    I am still working on the others.
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    Re: I am having difficulty finding the exact values within a given interval

    I cannot figure out question 2, find s if [-2pi, pi); tan^2 s = 3 because I am unsure how to treat the -2pi and pi rotation.

    Does anybody know how to solve this one?
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  5. #5
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    Re: I am having difficulty finding the exact values within a given interval

    First you should get the general solution for \displaystyle \tan^2{(s)} = 3, THEN work out which of those solutions fit in your region. What have you done for the general solution so far?
    Thanks from Odonsky
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    Re: I am having difficulty finding the exact values within a given interval

    So far I have tan (s) = sqrt(3) and know that tan = y/x
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    Re: I am having difficulty finding the exact values within a given interval

    In the first case you have tan x = (sqrt 3)/ 3 = 1/(sqrt 3)and it is the value of tan 30 degree or pi / 6

    what is the value of A if tan A = sqrt 3 It is 60 degree or pi/3
    also remember that tangent is positive in first and third quadrant and negative in 2nd and 4th quadrant.

    Quote Originally Posted by Odonsky View Post
    So far I have tan (s) = sqrt(3) and know that tan = y/x
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