Question

use the graph of y=sin2θ to find the value of sin 2θ for θ= pi/4 radians
A. -1
B. 0
C. 0.5
D. 1

Answer 1

for theta = pi/4
substitute pi/4 for tehta \[y=\sin(2\cdot \frac{\pi}{4})\]
simplify the fraction

Answer 2

and then graph the equation https://www.desmos.com/calculator
what is y when x=pi/4

Answer 3

1?

Answer 4

how would you find the period ?

Answer 5

I honestly don't know. I am so confused by this lesson

Answer 6

looks like you're just guessing
well here is the general equation \[\large\rm y=A \sin(Bx-C)+D\]
\[\left| A \right|\] is amplitude
\[P=\frac{2\pi}{B}\] 2pi because the wave repeats every 2 units (As you can see on the unit circle)
and C= horizontal shift
D= vertical shift

Answer 7

P=period use that equation to find the value of `B` when p=4pi

Answer 8

\[4\pi=\frac{2\pi}{B}\] solve for B
(B=the number at front of x variable )

Answer 9

I can't figure out what to put for B. I don't see a number before the x

Answer 10

so would it be B? since there is a 4 in it?

Answer 11

use the equation i gave to find B

Answer 12

we know that Period = 2pi/b
so since the given is period which is 4pi we can solve for b

Answer 13

\[ \color{Red}{P}=\frac{2\pi}{B}\]
\[ \color{Red}{4\pi}=\frac{2\pi}{B}\]
solve for B

Answer 14

y=2*sin(2*π-4)+π
y=π-2*sin(4)

Answer 15

no solve this equation for B \[ \color{Red}{P}=\frac{2\pi}{B}\]
\[ \color{Red}{4\pi}=\frac{2\pi}{B}\]
what is b = ?

Answer 16

given is Amplitude (which is 2) and the period (which is 4pi)
we don't have to deal with C and D

Answer 17

((4*π)/(2*π)) 2
((2*π)/(4*π)) 1/2

Answer 18

that's correct
B=1/2

Answer 19

btw in this example x is same thing as theta

Answer 20

so if B =1/2 how would you write the equation
with A=2 and B =1/2

Answer 21

y=0.5sin4θ

Answer 22

well amplitude is 2 for sure right ?? bec that is give so just replace A with 2
and we just found out that b =1/2 so replace b with 1/2

Answer 23

\[\huge\rm y=Asin b \theta\]
without vertical and horizontal shift

Answer 24

y=2sinθ/2?

Answer 25

yes

Answer 26

thank you so much

Answer 27

np