Inverse cosine with varriables

In summary, there is no known equation or method that can be used to find the area of a sector in terms of x and y without involving trigonometric functions. However, it is possible to use Pythagoras' theorem and the area formula for a triangle (base x height / 2) to find the area of the triangle in terms of x and y without using trig functions.
  • #1
kootromics
1
0
Is there any equation or method that can be used in place of a trigonomic function when side values of a triangle are known only as varriables? For example: triangle abc where c is the center of a circle and AC and BC are radiui who's value = x, and AB = x-2y. So far as I know, the area of this sector (ACB) can be found in terms of x and y but must contain a trigonomic function of x and y as well. ( such as (cos-1( x..y/x..y))(pie.r^2) . Is there any way to know the area of this sector simply in values of x and y without a trigonomic function?
 
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  • #2
Think of AB as the base the triangle. Use Pythagoras to determine the height of the triangle (draw a perpendicular from the center of the circle to the base - which bisects it!). Then you can write the area of the triangle (base X height / 2) in terms of x and y without the need for trig functions.
 
  • #3
I did something like that as well with A = ½ab.sinC and the cosine rule, but it's the area of the sector, rather than of the triangle he wants.
 

1. What is the inverse cosine function?

The inverse cosine function, denoted as arccos(x) or cos-1(x), is the inverse of the cosine function. It takes the output of the cosine function and gives the input value that produced it.

2. How is the inverse cosine function different from the regular cosine function?

The regular cosine function takes an angle (in radians) as an input and gives the ratio of the adjacent side to the hypotenuse of a right triangle as the output. The inverse cosine function takes a ratio as an input and gives the angle (in radians) that produced that ratio as the output.

3. Can the inverse cosine function have multiple solutions?

Yes, the inverse cosine function can have multiple solutions. This is because for a given ratio, there can be multiple angles that produce that same ratio. For example, cos-1(0.5) has two solutions: π/3 and 2π/3.

4. How are variables used in the inverse cosine function?

Variables can be used in the input of the inverse cosine function. For example, cos-1(x) represents the angle (in radians) that produces the ratio x. This allows us to solve for unknown angles in trigonometric equations.

5. What is the domain and range of the inverse cosine function?

The domain of the inverse cosine function is the set of all real numbers between -1 and 1, inclusive. The range of the inverse cosine function is the set of all angles (in radians) between 0 and π, inclusive.

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