Inverse trigonometric functions Puns

It is from our calculus I midterm so, it has to be basic solution. I tried to arccosx-pi/3= K then found cosK= (sqrt(3-3x^2)+x)/2 but it didn't helped. Can you guide me how to solve these kind of equations?

Evaluate the following limits or show they do not exist without using L’hospital’s rule.

As the title suggests, I'm trying to calculate inverse trigonometric functions on my Nspire CX II. It is set to Radian mode and is returning decimals instead of the radian value.

As an example, the inverse sin of -sqrt(2)/2 is returning -0.785398 instead of -pi/4

Is this a limitation of the CX vs the CX CAS?

Cross-posting from r/HomeworkHelp because I think they removed it.

I honestly do not know where to start. I understand from reading problem 1 that the upper bound of the range is y≤1 and the effect of absolute value on it, and that's about it. Checking a graphing calculator, the graph of the function is completely different from the standard inverse sine function we covered in class—the transformations only complicate things more.

I have not yet attempted problem 2: I'm hoping that I can tackle that myself once I understand the process of solving this type of problem.

Problems:

1. Find the domain and range of f(x) = 1 - 1/2 | arcsin(x^(2) - π ) |, algebraically.
2. a. Find the domain and range of f(x) = cot(2arccos x), algebraically
   b. Simplify the expression cot(2arccos x)

How do I calculate its value?

https://preview.redd.it/qsbwgps41ss61.jpg?width=109&format=pjpg&auto=webp&s=2fa1b1943e80b97ad044cd57c20e82ff4679eb19

I watched videos on youtube on inverse trigonometry but all I learned was to calculate values ( in degrees) for common radians like this:

https://preview.redd.it/d1ob80hb1ss61.png?width=206&format=png&auto=webp&s=b986f4108cc4f7b2427ad63a6588154dc4366688

1/5 is not a common value. How do I calculate for it without using a calculator?

Is the reason you cant use the general derivative inverse rule [f inverse prime(x) =1/f prime(x)] on trigonometric functions because they don't pass the horizontal line test, and thus aren't a "one-to-one function"?

Im confused how there is a sin(sin-¹ ½) if there is already such thing as sin-¹ ½

Please tell me why there is a sin beside a sin-¹. I also encountered this while learning the inverse of a cosine.

If you can, do tell me where I can watch videos that teach such problems (the one that has two sin or two cos)

I can't solve this problem from my workbook and it has left me go in circles. No pun intended. Does anyone has a simple way to solve it?.

The problem is in the figure from below.

https://imgur.com/a/BZRNgX4

https://i.imgur.com/kiVVhw2.png

If someone knows how to do it, It would be nice to get an explanation in layman terms.

INVERSE TRIGONOMETRIC FUNCTIONS AND TRIGONOMETRIC EQUATIONS

Solve for all real numbers x or angles with degree measure θ satisfying the equation and the indicated condition.

1. 6sin²x + 7sinx - 5 = 0, x ∈ [0°, 360°)

2. 2cos² x + 3cos x + 1 = 0, x ∈ [0°, 360°)

Please explain like I am 5 because I have shit for brains when it comes to math. I am trying to learn how to do inverse trig questions such as tan^-1(-sqrt3), however all of the explanations that my textbook gives me are very vague and I can barely grasp what they are trying to say, from what I understand I need to somehow make the function match the unit circle but I have no idea how to do that. Online resources have not made my situation better and I think may have made my situation worse.

Hi, I made quick review video for my students if they need a review of sine, cosine, tangent, their reciprocals, and all their inverses. My goal was to make a comprehensive and connected summary of the 12 functions without depending on very much previous knowledge. https://www.youtube.com/watch?v=UdopiUpZwP4

It's written in LaTex so that it's easy to read and anyone could print them out and make notes of their own. Slides are available here: Wordpress (download button): https://robbiepmath.wordpress.com/2020/10/13/precalculus-trigonometry-slides-notes/

Good Morning, I am hoping someone can help me solve this, but more importantly show me the steps. The problem is:

Csc (cos ^-1) ((√2)/3)

I need the exact value and not a long decimal, hope that makes sense!

https://preview.redd.it/lqlbecoa7tt51.png?width=531&format=png&auto=webp&s=564a12d539e71f319392565d8f41817ad52706d7