1. ## Help on my review: Link provided

Can somebody tell me how to do or at least give me the correct answers to a few problems here:

http://www.math.siu.edu/Finals/Fall11/109-web.pdf

#1 on page 6
#3 on page 8
#9 on page 4
#6 on page 2

Its the review for my precalc final and I need to understand those four... I really am just trying to power through this test because we are provided a note sheet that we can write.

Also a bonus: Find all solutions to the equation: 3(tan^2)x-1=0
The x is actually a theta on the review sheet.

2. ## Re: Help on my review: Link provided

Originally Posted by Ineedtopass
Can somebody tell me how to do or at least give me the correct answers to a few problems here:
You should really take the time to post the questions in the actual thread, rather than making us download a file from an external site. That would make it much easier to help you.

But, since I'm feeling generous...

I.6: The magnitude of a vector $\mathbf{v} = a_1\mathbf{i} + a_2\mathbf{j}$ is $\|\mathbf{v}\|=\sqrt{a_1^2+a_2^2}$.

The dot product of two vectors $\mathbf{u} = u_1\mathbf{i} + u_2\mathbf{j}$ and $\mathbf{v} = v_1\mathbf{i} + v_2\mathbf{j}$ is $\mathbf{u}\cdot\mathbf{v} = u_1v_1+u_2v_2$.

And the angle $\theta$ between two vectors is given by

$\cos\theta = \frac{\mathbf{u}\cdot\mathbf{v}}{\|\mathbf{u}\|\, \|\mathbf{v}\|}$.

(And this is easily generalized to higher dimensions)

I.9: Law of Sines
II.1: You have two right triangles. Use the given angles to find the measure of the non-right angles in both triangles. Then use trig to find the lengths of the two bottom sides. Their difference is the distance between the stadia.
II.3: Use the information provided to determine how far the pilot has flown in the wrong direction, then simply use the Law of Cosines to calculate the length of the side opposite the 10 degree angle.

3. ## Re: Help on my review: Link provided

Originally Posted by Ineedtopass
Also a bonus: Find all solutions to the equation: 3(tan^2)x-1=0
$3\tan^2\theta-1 = 0$

$\Rightarrow\tan^2\theta = \frac13$

$\Rightarrow\tan\theta = \pm\frac1{\sqrt3}$

Now, for which values of $\theta$ will $\tan\theta = \pm\frac1{\sqrt3}\mathrm?$