Question

Find a solution to the equation if possible.

NOTE: Give the answer in exact form and in decimal form.
1 = 81tan(8x + 9) - 8
Exact form: x _______

Answer 1

To solve the equation 1 = 81tan(8x + 9) - 8, we can isolate the variable x by adding 8 to both sides, dividing by 81, taking the inverse tangent, and solving for x.

Step-by-step explanation:

To solve the equation 1 = 81tan(8x + 9) - 8, we need to isolate the variable x. Here are the steps:

1. First, add 8 to both sides of the equation to get: 9 = 81tan(8x + 9)
2. Next, divide both sides by 81 to get: tan(8x + 9) = 9/81
3. Take the inverse tangent of both sides to get: (8x + 9) = tan^(-1)(9/81)
4. Now, subtract 9 from both sides of the equation to get the exact form of x: 8x = tan^(-1)(9/81) - 9
5. Finally, divide both sides by 8 to solve for x: x = (tan^(-1)(9/81) - 9)/8

In decimal form, you can use a calculator to evaluate the exact value of x or use an approximation of the inverse tangent.