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!

juriemagic Apr 16, 2023

#1**+1 **

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

Alan Apr 16, 2023

#2**0 **

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

#3**0 **

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?

Alan Apr 16, 2023

#4**0 **

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