# Trigonometry AS P1

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#1
May someone please explain this question to me?
It seems straightforward but I don't understand it sorry.

https://gyazo.com/c3ed58404f292f17280c4e115b20b3ff
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2 years ago
#2
Hi, you can think of this like y = bsinx a

It's a graph of 2sinx that's been moved up by 1, so a=1 and b=2 (If you move it all down by 1 you'll see that it is a normal sin graph, but goes between -2 and 2, so has been stretched upwards by times 2)

I don't know what the answer is, or if that's right, but that's what I'd put.

Sorry if that explanation was horrible lol, but hope that helps
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#3
Uhmm the answer is correct , but I dont understand it Its probably because I need to learn the trigonometric graphs, I can do all the trigonometic equations and identities questions without knowing the trig graphs tho...

What does the a and b supposed to be in the graph?

Thanks!
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2 years ago
#4
(Original post by Jian17)
Uhmm the answer is correct , but I dont understand it Its probably because I need to learn the trigonometric graphs, I can do all the trigonometic equations and identities questions without knowing the trig graphs tho...

What does the a and b supposed to be in the graph?

Thanks!
You are right - you do need to learn the shapes of the trig graphs. But this is really about linear transformation of a function. y = a + bsinx is a linear transformation of y = sinx with a vertical stretch factor of b and a vertical shift of a.
1
2 years ago
#5
Oh okay, no worries!

The +a is going to translate the graph vertically (so +1 will move the whole thing up by 1)

bsinx means that you'll have a sinx graph that has been stretched by b (so 2sinx means times all the y coordinates by 2)

Use BIDMAS, so you have to times the Y coordinates by 2 first and then shift the whole graph up by 1.

Sorry if this isn't making too much sense, someone much better at explaining than me should see this soon!
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2 years ago
#6
(Original post by Jian17)
May someone please explain this question to me?
It seems straightforward but I don't understand it sorry.

https://gyazo.com/c3ed58404f292f17280c4e115b20b3ff
I got 1+2sinx

The way I did it was by looking at the graph . I used the coordinate (0,1) to find a , then use coordinate (1/2pi,3) to find the value of b .
1
2 years ago
#7
(Original post by HelloImCool)
I got 1+2sinx

The way I did it was by looking at the graph . I used the coordinate (0,1) to find a , then use coordinate (1/2pi,3) to find the value of b .
I don’t know if this is the best way to approach it though. I just used simple algebra

I self quoted myself sorry
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#8
Thanks everyone for their help! I understand it better now, I will ask my teacher to explain it to me too when i can just to make sure i understand the concept tho
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#9
(Original post by HelloImCool)
I got 1+2sinx

The way I did it was by looking at the graph . I used the coordinate (0,1) to find a , then use coordinate (1/2pi,3) to find the value of b .
Why did you use the coordinate 1/2pi,3 to find b?? I can see why you used 0,1 but the other one :s
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2 years ago
#10
(Original post by Jian17)
Why did you use the coordinate 1/2pi,3 to find b?? I can see why you used 0,1 but the other one :s
You’re over complicating it.

y = sinx is a periodic function with a minimum value of -1 and a maximum value of +1. The difference between the two is 1 - (-1) = 2.

The transformation of y = sinx shown in the diagram is a periodic function with a minimum value of -1 and a maximum value of 3. The difference between the two is 3 - (-1) = 4. So the stretch factor b is .....
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2 years ago
#11
(Original post by Jian17)
Why did you use the coordinate 1/2pi,3 to find b?? I can see why you used 0,1 but the other one :s
3=1+b(sin(90)) —> sin 90 =1

3=1+b
2=b
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