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Urgent urgent maths help

Please could you explain how to do this:
If the exact value of sin 45= 1/root 2
What is the exact value of sin 135?
Ps this is without a calculator and I think it got something to do with the symmetry of the sin graph....
Thank you so much :smile:
Reply 1
Avatar for davros
davros
16
Original post by Cherrygrape1234
Please could you explain how to do this:
If the exact value of sin 45= 1/root 2
What is the exact value of sin 135?
Ps this is without a calculator and I think it got something to do with the symmetry of the sin graph....
Thank you so much :smile:

Your thought is correct! Do you know how to draw the graph? Do you know how sin (180 - x) relates to sin x?
Original post by Cherrygrape1234
Please could you explain how to do this:
If the exact value of sin 45= 1/root 2
What is the exact value of sin 135?
Ps this is without a calculator and I think it got something to do with the symmetry of the sin graph....
Thank you so much :smile:

Draw the graph for Y = Sin X in the interval 0 to 180.
then plot the known value and it should be obvious...
Original post by davros
Your thought is correct! Do you know how to draw the graph? Do you know how sin (180 - x) relates to sin x?

Ummmm I don’t think so...
Original post by mnot
Draw the graph for Y = Sin X in the interval 0 to 180.
then plot the known value and it should be obvious...

Yeah so if I plot sin 45 how do I get sin 135 from it? 🤔
Original post by Cherrygrape1234
Yeah so if I plot sin 45 how do I get sin 135 from it? 🤔

Hint: the graph of y = sin(x°) has a line of reflection symmetry at x = 90.
Reply 6
Avatar for davros
davros
16
Original post by Cherrygrape1234
Yeah so if I plot sin 45 how do I get sin 135 from it? 🤔

Are you working at A level? If you know the graph, the symmetry should make it obvious.

Also, you should know the formula for sin(A - B) which should in turn tell you what sin(180 - x) is equal to in terms of sin x.
Original post by Cherrygrape1234
Yeah so if I plot sin 45 how do I get sin 135 from it? 🤔

Lets imagine the curve y = Sin(x) in the region x=0 to x=180.
At both x = 0 & x = 180, y = 0. And this is obvious looking at the graph. At every point in this region (bar x = 90) for every value of y their are 2 solutions for x.
Now draw out the curve, plot the result for x = 45 and look at the relationship x at 135 has.
(edited 3 years ago)
Original post by MarkFromWales
Hint: the graph of y = sin(x°) has a line of reflection symmetry at x = 90.

Oh so would you add sin 45 to sin 90 (which has a value of 1) ....
Or sin 180 - sin 45?
(edited 3 years ago)
Original post by davros
Are you working at A level? If you know the graph, the symmetry should make it obvious.

Also, you should know the formula for sin(A - B) which should in turn tell you what sin(180 - x) is equal to in terms of sin x.

Nope I’m doing gcse
Original post by mnot
Lets imagine the curve y = Sin(x) in the region x=0 to x=180.
At both x = 0 & x = 180, y = 0. And this is obvious looking at the graph. At every point in this region (bar x = 90) for every value of y their are 2 solutions for x.
Now draw out the curve, plot the result for x = 45 and look at the relationship x at 135 has.

Ohhhh
I kinda get it now!
But which one?
You either do sin 45 + sin 90
Or sin 180 - sin 45?
:smile:
(edited 3 years ago)
Original post by Cherrygrape1234
Ohhhh
I kinda get it now!
You either do sin 45 + sin 90
Or sin 180 - sin 45?
:smile:

No, it's simpler than that. If you make a rough sketch of the graph of y = sin(x°) between x = 0 and x = 180 and mark in the line of symmetry you should just see the answer. (Going into your exam you will need to know the graphs of sine and cosine so you can sketch them instantly).
Original post by MarkFromWales
No, it's simpler than that. If you make a rough sketch of the graph of y = sin(x°) between x = 0 and x = 180 and mark in the line of symmetry you should just see the answer. (Going into your exam you will need to know the graphs of sine and cosine so you can sketch them instantly).

Umm I still don’t 😂
I did the symmetry and it is sin 90 = 1
Then how do I get the answer?
135 = 180 - 45

That should help
Original post by Cherrygrape1234
Umm I still don’t 😂
I did the symmetry and it is sin 90 = 1
Then how do I get the answer?

graph.jpg
Note: the red lines are mirror images of each other.
graph.jpg36.9KB
Original post by MarkFromWales
graph.jpg
Note: the red lines are mirror images of each other.

Thank you so much I finally understand!! :smile: :smile: :smile:
So the answer is 1/root 2 as well
Original post by Cherrygrape1234
Thank you so much I finally understand!! :smile: :smile: :smile:
So the answer is 1/root 2 as well

Yes.
Original post by MarkFromWales
Yes.

Ok thank you so much! ! :biggrin:

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