I need some help on understanding my math homework

[low path]

So, my teacher assigned us this homework that already has the results, you just need to get to it, and I´m a little bit stuck in some of this exercises..
They´re about the fundamental trigonometric formulas
The screenshot is in spanish tho, but I can translate it if needed..

[loud moon]

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[dusk gyro]

Do you need explanations with all the questions?

[queen whale]

Try to use the Pythagorean Identity, $\sin^2(x)+\cos^2(x)=1$. A little manipulation will help out.

[vale oriole]

Kocher

[queen whale]

(You can also build triangles for some of these questions; namely, 3-4-5 triangles, and then calculate the trig ratios based off them.)

[low path]

Well
Right now I´ve been trying harder and I manage to do mayority of them, but I´m still unable to do the C)-E) and G)

[low path]

I see
I´ll try that then

[low path]

Good Idea!
I´ll close this when I manage to finish everything

[dusk gyro]

May you translate the questions in English "as is", and post any attempt you have done?

[queen whale]

If you don’t mind, I can translate for you.

[dusk gyro]

Sure, I do not mind. Thank you.

[vale oriole]

Kocher

Kocher

Kocher

[queen whale]

@dusk gyro

[dusk gyro]

Thank you. I'll wait to see any attempt by @low path; if he/she still have questions with solving them.

[low path]

Hi!
Sorry for being late
A friend came in my house, but i´m free now

I had to rewrite in other paper because it´s pretty difficult to understand my notebook, and it´s even worse if I try to take a photo

[dusk gyro]

May you please review these issues and address?
(1.) What is sen? Is it the same as "sin (sine)"?

(2.) Work on your writings
(i.) For (c.) Is that "tan x"?

(3.) For (c.), the LHS of the 3rd line is incorrect.
How can $\cos x = \sqrt{1 - \cos x^2}$? What Trigonometric Identity/Formula is it?

(4.) For (G.), what is R?
Is it not better to define the variables that you use?
Also, what is the need for the exclamation mark? You do know that the exclamation mark represents factorials...right?

...among several other issues.

Also, for several questions on trigonometry, you can check the solution with the graphing calculator (if your professor allows the use of a graphing calculator).

Be it as it may, here are the detailed solutions.
Numbers (16.) and (17.) on:
https://examssuccess.appspot.com/MATHEMATICS/Trigonometry.html#one-twenty
I think I explained it well. But, if there is anything you do not understand regarding the explanations/solutions, please let me know.

[vale oriole]

The Mathematics Guy
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[low path]

Well, let´s see..
Sin and sen are the same, tan and tg are also the same, I think the issue there is because of language.
R means Result
The teacher already gived us the results, I just need to actually get there, and sorry for the exclamation mark, my bad.
And no, I don´t use the graphing calculator, I use the scientific one
And about that formula, I was trying to clear "sin", with the new formulas that I´ve been using along the exercises, I saw one of my classmates doing it, and he got the right answer, but I get stuck in the same place.

So i saw the exercises in the link that you sand me, I see, throught I don´t think the teacher wants us to use the angles, but yeah, thanks!, i´m done with my work

One last think
How do I use the "Mathematics rank bot" to thank you?

[queen whale]

You type +close

[low path]

+close

[winter sand]

Please thank your Helpers before closing!

Please thank the helpers who assisted you by clicking the buttons below. You can thank each helper only once. Once you're done, click "Close Post" to close this thread.

[dusk gyro]

You may click the link: "Thank The Mathematics Guy".
I also suggest you click the link: "Thank Kocher" because he gave you hints and also translated the question for me.
Thank you.

[winter sand]

Thank you for your feedback! The Mathematics Guy has been awarded 1 . They now have 1 . They have 3 daily left for today.

[winter sand]

Thank you for your feedback! Kocher has been awarded 1 . They now have 1245 . They have 1 daily left for today.

[low path]

Oh, I see
Thanks!