1. ## Sine function problem

Here's a problem that I have to do for my pre-cal class:
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An architect is using a computer program to design the entrance of a railroad tunnel. The outline of the opening is modeled by the function f(x) = 8 sin x + 2, in the interval 0 ≤ x ≤ pi, where x is expressed in radians.

Solve algebraically for all values of x in the interval 0 ≤ x ≤ pi, where the height of the opening, f(x), is 6. Express your answer in terms of pi.

If the x-axis represents the base of the tunnel, what is the maximum height of the entrance of the tunnel?
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I thought I should set f(x) to 6 and solve the equation, which I did, and I got 30 as my answer. But that doesn't make sense because the answer is supposed to expressed in terms of pi, and is supposed to be less than pi. I don't know how else to solve this problem, if anyone could help that would be great! Thanks

$\displaystyle 30^{\circ} = \frac{\pi}{6}$

don't forget that there is another angle where $\displaystyle \sin{x} = \frac{1}{2}$ in quad II

3. Originally Posted by francesgw
Here's a problem that I have to do for my pre-cal class:
----------------
An architect is using a computer program to design the entrance of a railroad tunnel. The outline of the opening is modeled by the function f(x) = 8 sin x + 2, in the interval 0 ≤ x ≤ pi, where x is expressed in radians.

Solve algebraically for all values of x in the interval 0 ≤ x ≤ pi, where the height of the opening, f(x), is 6. Express your answer in terms of pi.

If the x-axis represents the base of the tunnel, what is the maximum height of the entrance of the tunnel?
----------------

I thought I should set f(x) to 6 and solve the equation, which I did, and I got 30 as my answer. But that doesn't make sense because the answer is supposed to expressed in terms of pi, and is supposed to be less than pi. I don't know how else to solve this problem, if anyone could help that would be great! Thanks
Think pi-radians and not degrees Ya - what skeeter said!

4. Ohhhh! Hahahah. I can't believe I forgot about converting to radians.. this problem was from a review sheet and I haven't done this type of math in a while. I'm glad I reviewed it! Thanks guys

5. oh wait! what about the second part of the problem, how to find the maximum height of the tunnel? If the function was just 8 sin x then I think it would be 8, but since it's 8 sin x + 2 I'm not sure where the 2 figures in. Would that make it 10? Or I could be completely off. How do you find the max. height of the tunnel?

6. what is the max value that sinx can be?

7. ahhh i don't know! I don't know whether it's in degrees or radians or what.. I mean the max value of a graph of sinx would be 1.. but i don't think that's the answer you're looking for.

8. okay the max value of sinx is one. So if we plug that into the equation, 8 sinx +2: 8*1+2= 10. Is the maximum 10?

9. yes ... the max is 10.

10. 8?

I haven't done pre-calc in a while, but if the max value of $\displaystyle \sin(x)$ is 1 then the max $\displaystyle sin(x)+2$ can be is 1, $\displaystyle 1 \cdot8=8$.

11. Originally Posted by OnMyWayToBeAMathProffesor
8?

I haven't done pre-calc in a while, but if the max value of $\displaystyle \sin(x)$ is 1 then the max $\displaystyle sin(x)+2$ can be is 1, $\displaystyle 1 \cdot8=8$.
the expression is 8sinx + 2

12. Edit: Sorry, you already said this. Nevermind.
ok, the maximum value of sin(x) is one. So if we plug that into the equation, $\displaystyle 8\sin(x)+2= 8\times1+2= 10$

13. I am sorry, i thought the equation was $\displaystyle 8\sin(x+2)$ not $\displaystyle 8\sin(x)+2$. so 10 then?