Why is cos^-1 used in the first example but not the second?

[PhyiscsisNeat]

Mentor note: Thread moved from a homework section.
I don't know if this is the right forum, but this isn't really a homework question that I have to solve, I am just trying to get better with vectors/trig and I looked at this for basic examples. I am okay with finding x and y components, but I am unsure why the woman in the video used cos^-1 in the first example to find an angle but not in the second. She breaks the second example down into one nice and neat right triangle and has all the values for all three sides in meters but doesn't use cos^-1 in the second example as she did in the first, despite having all values for each side? Can anyone clarify for me?

 

[PeroK]

She ends up with $\cos \theta$ in the second example as well. Then she says what this makes $\theta$. I guess she didn't mention taking $\cos^{-1}$ explicitly because she assumed you'd know that that is how to get from $\cos \theta$ to $\theta$, as she showed you in the first example.

 

[PhyiscsisNeat]

She ends up with $\cos \theta$ in the second example as well. Then she says what this makes $\theta$. I guess she didn't mention taking $\cos^{-1}$ explicitly because she assumed you'd know that that is how to get from $\cos \theta$ to $\theta$, as she showed you in the first example.

I have no idea what you just said and I would very much like to understand why she uses cos^-1 in the first and cos in the second

 

[PeroK]

I have no idea what you just said and I would very much like to understand why she uses cos^-1 in the first and cos in the second

In both cases she has $\cos \theta =$ something.

In the first example, she says $\theta = cos^{-1}$ of that something and does the calculation

In the second example, she simply misses out that statement and tells you what she calculated $\theta$ to be. She assumed that you could work out for yourself that to go from $\cos \theta$ to $\theta$ you use $\cos^{-1}$. She doesn't have to tell you every time!

In other words, you are not going to be told every step in every calculation every time.

 

[PhyiscsisNeat]

In both cases she has $\cos \theta =$ something.

In the first example, she says $\theta = cos^{-1}$ of that something and does the calculation

In the second example, she simply misses out that statement and tells you what she calculated $\theta$ to be. She assumed that you could work out for yourself that to go from $\cos \theta$ to $\theta$ you use $\cos^{-1}$. She doesn't have to tell you every time!

In other words, you are not going to be told every step in every calculation every time.

Thanks. So she used cos^-1 the second time as well but just didn't show it?? I googled when to use inverse trig functions and found:

"Inverse Sine, Cosine and Tangent. The inverse trigonometric functions (sin-1, cos-1, and tan-1) allow you to find the measure of an angle in a right triangle. All that you need to know are any two sides as well as how to use SOHCAHTOA."

I'm about to start the second part of an algebraic physics course/simple mechanics class and vectors have been confusing me but I think this helps a lot (if I'm reading it correctly). I can solve the word problems with algebra all day until I pass out, but throw vectors in there and I'm confused. I know how important vectors are so I hope I have figured it out. Thank you for the replies.