Evaluate
Tan[(3pi-70000pi)/2]
(3pi - 70000pi)/2 = 3pi/2 - 350000pi
so, since it's a multiple of pi away from 3pi/2,
tan[(3pi - 70000pi)/2] = tan(3pi/2) = undefined
To evaluate the trigonometric expression tan((3π - 70000π)/2), we need to simplify the given expression first.
Let's start by simplifying the angle inside the tangent function:
(3π - 70000π)/2
Taking out common factors, we have:
(-69997π)/2
Now, let's simplify the numerator by dividing by 1000:
(-69997π)/2 = -34.9985π
The denominator remains the same.
Next, we need to simplify the angle to its equivalent within the range of [0, 2π). To do this, we subtract multiples of 2π until we get a number within the desired range.
Since π is approximately 3.14159, we have:
-34.9985π ≈ -34.9985 * 3.14159 ≈ -109.96298
Now we have an angle of -109.96298.
Finally, we evaluate the tangent function using a calculator:
tan(-109.96298) ≈ -2.7475
Therefore, the value of tan((3π - 70000π)/2) is approximately -2.7475.
To evaluate the given expression tan[(3π-70000π)/2], we can follow these steps:
Step 1: Simplify the argument inside the tangent function.
The first step is to simplify the argument inside the tangent function, which is (3π - 70000π)/2.
Note that π is a constant equal to approximately 3.14159.
So, we can simplify the expression as follows:
(3π - 70000π)/2 = (-69997π)/2
Step 2: Divide the numerator by the denominator.
In this case, the numerator is -69997π and the denominator is 2.
By dividing these two, we get:
(-69997π)/2 = -34998.5π
Step 3: Replace π with its numerical approximation.
Since we are dealing with a numerical approximation, we can replace π with its value approximately as 3.14159.
Thus, -34998.5π ≈ -34998.5 * 3.14159.
Step 4: Calculate the result.
Multiplying the approximate value of π by -34998.5 gives us:
-34998.5 * 3.14159 ≈ -109981.6885.
So, tan[(3π-70000π)/2] ≈ tan(-109981.6885).
The final approximation may vary depending on the level of precision required.