Question

The functions f(theta) and g(theta) are sine functions, where f(0) = g(0) = 0. The amplitude of f(theta) is twice the amplitude of g(theta). The period of f(theta) is one-half the period of g(theta). If g(theta) has a period of 2pi, and f(pi/4) = 4, write the function rule for g(theta).

Answer 1

@satellite73

Answer 2

@amistre64 @freckles

Answer 3

@dan815

Answer 4

@TheSmartOne @confluxepic @Nnesha

Answer 5

Can you help?

Answer 6

that hurts my brain ..

Answer 7

Yeah, tell me about it..

Answer 8

canyou organize the data in a more convenient manner?

Answer 9

what do we know pull it apart and use t not theta ... the less letters the better

The functions f(t) and g(t) are sine functions,

where f(0) = g(0) = 0.

The amplitude of f(theta) is twice the amplitude of g(theta).

f(t) = 2 g(t)

The period of f(t) is one-half the period of g(t). f is twice as fast as g

f(2t) = 2 g(t)


If g(t) has a period of 2pi, then g is a normal sin function

and f(pi/4) = 4, write the function rule for g(theta).

2t = pi/4 when t = pi/8

Answer 10

okay

Answer 11

so when 2 g(pi/8) = f(pi/4) = 4

Answer 12

how'd you get that, and why?

Answer 13

i wrote it all out .... what part do you get lost on?

Answer 14

this part:
"The period of f(t) is one-half the period of g(t). f is twice as fast as g

f(2t) = 2 g(t)


If g(t) has a period of 2pi, then g is a normal sin function

and f(pi/4) = 4, write the function rule for g(theta).

2t = pi/4 when t = pi/8"

Answer 15

if we cover the same distance in half the time, are we going faster or slower?

Answer 16

faster

Answer 17

how'd you get \(f(2\theta)= ~2~ g(\theta)\)?

Answer 18

f completes a cycle in say a time of 1, g completes a cycle in a time of 2

f is 2 times as fast as g.

f(2t) for a given t value is relative to g(t)

sin(2t) is twice as fast (takes half the time) or rather it completes 2 cycles when sin(t) completes 1 cycle

Answer 19

do we agree that the arguements are sin(2t) and sin(t) ?

Answer 20

sin(pi/2) = 1

sin(2(pi/4)) = 1

pi/4 is half of pi/2

Answer 21

okay, I get that..

Answer 22

half the period is twice as fast.