# Thread: I am having difficulty finding the exact values within a given interval

1. ## 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?

2. ## 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.

3. ## Re: I am having difficulty finding the exact values within a given interval

Originally Posted by chiro
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.

4. ## 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?

5. ## Re: I am having difficulty finding the exact values within a given interval

First you should get the general solution for $\displaystyle \displaystyle \tan^2{(s)} = 3$, THEN work out which of those solutions fit in your region. What have you done for the general solution so far?

6. ## 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

7. ## 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.

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

,

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### how to find all values of theta in the interval ​ [0 degrees°​,360degrees°​)

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