Express y = arccos x in terms of y

Thread starter thomas49th
Start date Sep 14, 2008
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In summary, "Expressing y = arccos x in terms of y" means finding a way to write the inverse cosine function in a form where the output is y instead of x. This allows us to solve for y in terms of x instead of the other way around. It is important to express y = arccos x in terms of y because it allows us to solve for the value of y, which can be useful in many applications such as solving equations, finding angles, and graphing functions. The steps to express y = arccos x in terms of y are to isolate the inverse cosine function, use the inverse property of cosine, and simplify the expression. Not any value of x can be used in the expression

Sep 14, 2008

thomas49th

Homework Statement

Give that:

y = arccosx -1<= x <= 1 and 0 <= y =< pi

a) express arcsin xin terms of y

Homework Equations

The Attempt at a Solution

Well I am given arccos x and i need to convert to arcsin x ?

Thanks :)

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Sep 14, 2008

armis

Hi thomas49th

Just plot the functions and all should become clear

1. What does "Express y = arccos x in terms of y" mean?

Expressing y = arccos x in terms of y means finding a way to write the inverse cosine function in a form where the output is y instead of x. This allows us to solve for y in terms of x instead of the other way around.

2. Why is it important to express y = arccos x in terms of y?

Expressing y = arccos x in terms of y allows us to solve for the value of y, which can be useful in many applications such as solving equations, finding angles, and graphing functions.

3. What are the steps to express y = arccos x in terms of y?

To express y = arccos x in terms of y, we first need to isolate the inverse cosine function on one side of the equation. Then, we use the inverse property of cosine to rewrite the equation in terms of y. Finally, we simplify the expression to get y = arccos x in terms of y.

4. Can any value of x be used in the expression y = arccos x in terms of y?

No, the value of x must be between -1 and 1 for the inverse cosine function to have a real output. This is because the range of the inverse cosine function is restricted to 0 ≤ y ≤ π.

5. How is the graph of y = arccos x related to the graph of y = cos x?

The graph of y = arccos x is the reflection of the graph of y = cos x over the line y = x. This means that the x and y values of each point on the two graphs are swapped. Additionally, the domain and range of the two functions are also swapped.