Solving Trigonometric Equations

[BlackOut07]

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?

 

[Mark44]

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.

 

[BlackOut07]

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

 

[gordonj005]

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?

 

[BlackOut07]

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)

 

[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)

 

[BlackOut07]

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 :/

 

[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.

 

[BlackOut07]

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.

 

[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.

 

[BlackOut07]

i still don't understand to be honest :/