
How do you solve ?
Answer
463.2k+ views
Hint: We try to solve the equation with the help of graphical point of view and using the interval of range for the trigonometric function . We know the range for the function is . This gives the interval for the intersecting point for the equation .
Complete step by step answer:
We use the approximation theorem to find the point.
We try to solve the equation through the graph and use the interval of range.
We know that the primary interval of domain for is but the range is .
So, if there is any intersection point for , it has to be in the interval of .
Now we try to take the functions as .
We got two equations and put them as and .
We can see there is only one intersection between these curves.
Now we take the new function of .
Differentiating both sides, we get .
Now we apply Newton’s method of approximation where .
We put the values of the approximation as the terms of .
The approximation value goes to .
The value also matches with the point with the graph.
Therefore, the sole intersecting point for the equation is . (approx.)
The solution for the is .
Note:
We can also use the function where . These types of functions give the difference between the points using the slope value of the function to reduce the error part. We can put the consecutive values in the theorem of .
Complete step by step answer:
We use the approximation theorem to find the point.
We try to solve the equation
We know that the primary interval of domain for
So, if there is any intersection point for
Now we try to take the functions as
We got two equations and put them as

We can see there is only one intersection between these curves.
Now we take the new function of
Differentiating both sides, we get
Now we apply Newton’s method of approximation where
We put the values of the approximation as the terms of
The approximation value goes to
The value also matches with the point with the graph.
Therefore, the sole intersecting point for the equation
The solution for the
Note:
We can also use the function where
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