For what value of θ (to the nearest degree) is the error in sinθ ≈ θ approximately 5%?

31°

Step-by-step explanation:

Comparing θ and sin(θ) really only makes sense when both are expressed in radians. A graphing calculator shows θ/sin(θ) = 1.05 for θ ≈ 0.538 radians. That angle value is approximately 30.8 degrees.

θ ≈ 31° when the error in sin(θ) ≈ θ is 5%.

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Check

31° ≈ 0.541 radians

sin(31°) ≈ 0.515

The difference between these values is about 5.05% of sin(31°).

step-by-step explanation:

if you want to solve percent error follow these steps.

1. subtract the accepted value from the experimental value.

2. take the absolute value of step 1.

3. divide that answer by the accepted value.

4. multiply that answer by 100 and add the % symbol to express the answer as a percentage.

if you want to solve percent of change just do this.

1. work out the difference (increase) between the two numbers you are comparing.

2. divide the increase by the original number and multiply the answer by 100. if your answer is a negative number then this is a percentage decrease.

hope this : )