Final answer:
To find the exact value of tan[sin⁻¹(8/9)], take the tangent of the angle sin⁻¹(8/9). The approximate value is 2.086.
Step-by-step explanation:
To find the exact value of tan[sin⁻¹(8/9)], we need to use the properties of inverse trigonometric functions. Let's start by finding the angle sin⁻¹(8/9). This angle represents the angle whose sine value is 8/9.
Using a calculator, we find that sin⁻¹(8/9) ≈ 64.06°.
Next, we can find the value of tan[sin⁻¹(8/9)] by taking the tangent of the angle we just found. Using a calculator, we have tan(64.06°) ≈ 2.086.
Therefore, the exact value of tan[sin⁻¹(8/9)] is approximately 2.086.