SOLUTION: Hi all, I'm currently doing my math homework and I'm stuck on a single question. If you can help me with the question, that would be awesome : Find the values of each pair of exp

Algebra ->  Trigonometry-basics -> SOLUTION: Hi all, I'm currently doing my math homework and I'm stuck on a single question. If you can help me with the question, that would be awesome : Find the values of each pair of exp      Log On


   

Question 873858: Hi all, I'm currently doing my math homework and I'm stuck on a single question. If you can help me with the question, that would be awesome :
Find the values of each pair of expressions.
1.) sin 80, cos 10
2.) cos 25, sin 65
What do you notice about the values and the angles in each pair?
Explain why your answers make sense.
The answers in each set are equal to each other (sin 80= the same answer as cos 10) however I don't know what is the connection between them. Again, if you can help, that would be awesome :)!
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
Since 80%5Eo%2B10%5Eo=90%5Eo and 25%5Eo%2B65%5Eo=90%5Eo ,
those pairs of angles could be the acute angles in right triangles.
The same ratio leg%2Fhypotenuse that is the sine of one angle
is also the cosine off the other angle.
When two angles add up to 90%5Eo (when they are complementary),
the sine of one angle is the cosine of the other angle.
In formulas,
sin%2890%5Eo-x%29=cos%28x%29 and cos%2890%5Eo-x%29=sin%28x%29

x=x%2F1=sin%2865%5Eo%29=cos%2825%5Eo%29 y=y%2F1=sin%2825%5Eo%29=cos%2865%5Eo%29