how do I do these questions?

HELP: Since this is a transcendental equation, you cannot solve it algebraically. You could solve it graphically, but the easiest approach is just to solve it numerically.

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

For what value of θ (to the nearest degree) is the error in sinθ ≈ θ approximately 1%?

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

For what value of θ (to the nearest degree) is the error in tanθ ≈ θ approximately 1%?

For what value of θ (to the nearest degree) is the error in cosθ ≈ 1 - θ2/2 approximately 5%?

For what value of θ (to the nearest degree) is the error in cosθ ≈ 1 - θ2/2 approximately 1%?

please give me the rules for solving these. thanks i will give points to all.

## Answers (1)

Do you have Excel? If so, click on Tools and see if the solver option is available. If not, use Tools->AddIns to make it available.

An example of how to do this is to put the angle, in radians, in cell A1. Try 0.6 as a guess. Then compute the sin in cell b1 (that is, enter "=sin(a1)". Next, compute the absolute value of the error in cell c1 (enter "=ABS(A1-B1)/(2*(A1+B1))"

Go into Tools, then pick solver. Tell it you want to make the value of cell C1 to be 0.05 (for the 5% case). Tell it to adjust cell A1 to accomplish this. Click the solve button.

You will be asked if you want to accept the solution; you should accept it. Cell A1 will now have the angle (in radians) that makes the error 5%. Convert the angle to degrees, and round to the nearest degree. (For this example, the radian value should be about 1.075

As for solving the problem numerically, that is what the Excel solver does. It trys a guess, makes a second guess, and observes if the second guess is better than the first. If so, it moves further in that direction; otherwise it tries in the opposite direction. If one guess is too high, and one is too low, it picks a guess in-between. It continues this process until the answer is close enough (in your case the answer would be close enough when the difference between the last guess and the next-to-last guess is less than 0.5 degrees, or 0.008 radians).

Reference:Excel help.