Final answer:
To approximate sin31∘ using linearization techniques, we can use the small angle approximation. The approximation is not very close to the exact answer obtained using a calculator.
Step-by-step explanation:
To approximate sin31∘ using linearization techniques, we can use the small angle approximation. For small angles, the sine of the angle can be approximated by the angle itself in radians. Since 31 degrees is a relatively small angle, we can approximate it as 31/180π radians. Therefore, sin31∘ ≈ 31/180π ≈ 0.171.
To compare this approximation to the exact answer obtained using a calculator, we can calculate the exact value of sin31∘ using a calculator. The exact value is approximately 0.515.
The approximation using linearization techniques is not very close to the exact answer obtained using a calculator. The approximation is off by about 0.344.