# Solving Trigonometric Equations

## Homework Statement

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?

## The Attempt at a Solution

1) i'm not sure how to approach/solve this question

2) i got 0, can anyone confirm?

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## Homework Statement

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?

## The Attempt at a Solution

1) i'm not sure how to approach/solve this question
Start by sketching a graph. At what points on the graph is the height above the starting position 1 cm?
2) i got 0, can anyone confirm?
Show us how you got 0.

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

a=(5sin120pi(1))-(5sin120pi(0.999))/(1-0.999)
=0?? doesn't make sense though
What you have calculated here is the current at t = 1. Is the question not asking for the rate of change at t = 1?

What you have calculated here is the current at t = 1. Is the question not asking for the rate of change at t = 1?
so would it be
a=(5sin120pi(1.001))-(5sin120pi(0.999))/(1.001-0.999)

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)

Yes, that's a pretty close approximation. Question, have you ever done any calculus before?
no, i have it second semester.

and the answer is STILL 0 :/

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.

## Homework Statement

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).
the maximum of this graph is 0.25 :/

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.
i got the answer as a=-328.365.

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.

i still don't understand to be honest :/