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# Sin22

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Hi friends,

trust you are all doing well...please just  quick guidance with this problem?

If Sin22 = k, use a diagram to determine Cos158 in terms of k

My problem is that if the angle is given a  $$\theta$$ for example, I can do the sum, I'm just not sure how to work with a given angle?..Thank you very much indeed!

Apr 16, 2023

#1
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cos(158) = cos(180 - 22) = cos(180)*cos(22) + sin(180)*sin(22) = -cos(22) = -√(1-sin(22)^2) = - √(1 - k^2)

Apr 16, 2023
#2
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Hi Alan,

Yes, I worked on it and kinda got it right, thank you klindly, however, maybe just one that I do not see how to go about is to calculate Sin11?...Must I devide Sin22 by 2 and then proceed, in which case I'm not sure how to?..or is it an entirely different approach?..please if you don't mind..

juriemagic  Apr 16, 2023
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Note that cos(22) = √(1 - k^2)  from the previous result.

Also cos(22) = cos(11 + 11) = 1 - 2*sin(11)^2

Can you take it from there?

Apr 16, 2023
#4
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Hi Alan,

I see, so I then say

$$Cos22=Cos2(11)$$

$$Cos22=1-2Sin^211$$

$$\sqrt{1-k^2}=1-2Sin^211$$

$$2Sin^211=1-\sqrt{1-k^2}$$

$$Sin11=\sqrt{1-\sqrt{1-k^2} \over2}$$

I think this might be it?

juriemagic  Apr 16, 2023
#5
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Yes, except you should put cos(2*11)  rather than cos2(11).

Alan  Apr 17, 2023
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Oh yes, I see....Thanks a mill Alan

juriemagic  Apr 17, 2023