# Solving Trigonometric Equations

1. Nov 17, 2011

### BlackOut07

1. The problem statement, all variables and given/known data

1) When a pendulum 0.5m long swings back and forth, its angular displacement Ɵ from rest position, in radians is given by Ɵ=1/4sin((pi/2)t), where t is the time, in seconds. At what time(s) during the first 4 s is the pendulum displaced 1 cm vertically above its rest position? (assume the pendulum is at its rest position at 0).

2) the current in a household appliance varies according to the equation A=5sin120pit, where A is the current in amperes, and t is the time, in seconds. at what rate is hte current changing at t=1s?

3. The attempt at a solution
1) i'm not sure how to approach/solve this question

2) i got 0, can anyone confirm?

2. Nov 17, 2011

### Staff: Mentor

Start by sketching a graph. At what points on the graph is the height above the starting position 1 cm?
Show us how you got 0.

3. Nov 17, 2011

### BlackOut07

a=(5sin120pi(1))-(5sin120pi(0.999))/(1-0.999)
=0?? doesn't make sense though

4. Nov 17, 2011

### gordonj005

What you have calculated here is the current at t = 1. Is the question not asking for the rate of change at t = 1?

5. Nov 17, 2011

### BlackOut07

so would it be
a=(5sin120pi(1.001))-(5sin120pi(0.999))/(1.001-0.999)

6. Nov 17, 2011

### gordonj005

Yes, that's a pretty close approximation and will give you an answer within 2.35 % of the exact answer. Question, have you ever done any calculus before? (and yes, I do realize this is the precalculus section)

7. Nov 17, 2011

### BlackOut07

no, i have it second semester.

and the answer is STILL 0 :/

8. Nov 17, 2011

### gordonj005

I assure you the answer is not zero, make sure your calculator is in radian mode, and make sure you keep track of your negatives.

9. Nov 17, 2011

### BlackOut07

the maximum of this graph is 0.25 :/

i got the answer as a=-328.365.

10. Nov 17, 2011

### gordonj005

For the pendulum, think in terms of trigonometric functions. If you set the rest position to (0, 0) and you know the radius is 0.5 m, for what values of $\theta$ will the height be 1 cm? Once you figure that out, you can find the times fairly easily.

Ok so:

$$m = \frac{5 \sin{120\pi 1.001} - 5 \sin{120\pi 0.999}}{0.002}$$
$$m = 2500(\sin{120.12 \pi} - \sin{119.88 \pi})$$

where $\sin{120.12 \pi} \approx 0.368$ and $\sin{120\pi 0.999} \approx -0.368$. I think if you try again you'll get the right answer.

11. Nov 17, 2011

### BlackOut07

i still don't understand to be honest :/