Evaluate the following expressions

tan(−22/15π)

tan(-22/15π)

-tan(22/15π)
-tan(π+7/15π)
-tan(7/15π)
not a recognizable value. As long as you have to use your calculator anyway, why nut just plug in the original value? You get -9.514

Or is there more to the question than what you posted?

There is more to it...

Find the exact value

tan^-1(tan(-22/15pi))

I just could not figure out how to find an exact value for tan(-22/15pi)

You don't need it.

arctan(-x) = -arctan(x)
So, now you want

arctan(-tan(7/15π))
= -arctan(tan(7/15π))
= -7/15π

To evaluate the expression tan(-22/15π), we can follow these steps:

Step 1: Convert the angle from radians to degrees.
To convert from radians to degrees, we multiply the given angle by 180/π. In this case, we have -22/15π radians.
-22/15π * (180/π) = (-22/15) * 180 ≈ -251.33 degrees

Step 2: Find the reference angle.
The reference angle is the positive acute angle between the terminal side of the angle and the x-axis (in standard position). Since tanθ = y/x, we only need the reference angle.

Step 3: Determine the quadrant.
Since the angle is in degrees, we can look at the sign of the angle to determine the quadrant:
- A negative angle is in the third or fourth quadrant.
- A positive angle is in the first or second quadrant.

In this case, since -251.33 degrees is negative, it lies in the third quadrant.

Step 4: Calculate the reference angle in the appropriate quadrant.
In the third quadrant, we take the supplementary angle (180 degrees) and subtract the angle (-251.33 degrees) to find the reference angle.
Reference angle = 180 - (-251.33) = 180 + 251.33 ≈ 431.33 degrees

Step 5: Find the tangent value.
Now that we have the reference angle (431.33 degrees), we can find the tangent of that angle.

To find the tangent of an angle, we can use a calculator or reference charts. The tangent function is defined as the ratio of the opposite side to the adjacent side in a right triangle.

So, plug in the reference angle (431.33 degrees) into a calculator or use a reference chart to find the tangent value:
tan(431.33 degrees) ≈ -1.20

Therefore, the value of tan(-22/15π) is approximately -1.20.