Solve for Int: cos(x)=cos(17π/5)

  • Thread starter Karma
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In summary, the cosine of (x+n2pi) is equal to the cosine of x. In this specific case, the value of x is (7pi/5) because cosine is periodic with a period of 2pi and adding 2pi to the argument results in the same value. This can also be seen by converting 17pi/5 to the equivalent value of (7pi/5) using basic fraction addition.
  • #1
Karma
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sin-(cos(17pi/5))

cos=(x+n2pi)=cos(x)

I know that this becomes 7pi/5.. But what is substituted for the integer value? and why? (how does it become 7pi/5)
 
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  • #2
because cosinus is periodic with period 2pi. So if you add 2pi in the argument you get the same result.
 
  • #3
Karma said:
sin-(cos(17pi/5))

cos=(x+n2pi)=cos(x)
It's not at all clear what you mean by "sin-(cos(17pi/5)". do you mean 'sine or cosine of that'? And, of course the "=" in "cos=" is a typo.

17/5= 3 and 2/5= 2+ (1+ 2/5). The "n" in "n2pi" is 1 and the "x" is (1+ 2/5)pi= (7pi/5).
 
  • #4
Karma said:
sin-(cos(17pi/5))

cos=(x+n2pi)=cos(x)
It's not at all clear what you mean by "sin-(cos(17pi/5)". do you mean 'sine or cosine of that'? And, of course the "=" in "cos=" is a typo.

17/5= 3+ 2/5= 2+ (1+ 2/5). The "n" in "n2pi" is 1 and the "x" is (1+ 2/5)pi= (7pi/5).
 

1. What does "Int" stand for in this equation?

"Int" stands for "integer," which is a whole number with no fractional or decimal part. In this equation, we are solving for the integer values of x that satisfy the given cosine function.

2. What is the general process for solving this type of equation?

The general process for solving equations involving trigonometric functions is to use inverse trigonometric functions to isolate the variable and then solve for it. In this case, we would use the inverse cosine function (arccos) to find the value of x that satisfies the equation.

3. Is there more than one solution to this equation?

Yes, there can be more than one solution to this equation. Since cosine is a periodic function, it has multiple solutions for a given input. In this case, there are infinitely many solutions for x that satisfy the equation.

4. How can I check if my solution is correct?

You can check your solution by plugging it back into the original equation. If the resulting equation is true, then your solution is correct. Additionally, you can use a graphing calculator to visually see where the two functions intersect, which would represent the solutions to the equation.

5. Can this equation be solved algebraically?

No, this equation cannot be solved algebraically. In most cases, equations involving trigonometric functions cannot be solved algebraically and require the use of inverse trigonometric functions or a graphing calculator to find the solutions.

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