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?

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.

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

Quote:

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.

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?

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?

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

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** So far I have tan (s) = sqrt(3) and know that tan = y/x