anonymous
  • anonymous
what are the steps I need to take to answer these questions Find the exact value of each expression. Do not use calculator cos(sin^-1(3/5)) and Find exact value of the expression sin(cos^-1 (5/13)-cos^-1 (4/5))
Mathematics
jamiebookeater
  • jamiebookeater
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freckles
  • freckles
you could let u=arcsin(3/5) so sin(u)=3/5 and you are trying to find cos(u) given sin(u)=3/5 |dw:1436832595334:dw|
freckles
  • freckles
that one thing is suppose to be u
freckles
  • freckles
the second one I would expand and make two right triangles

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freckles
  • freckles
expand using: \[\sin(a-b)=\sin(a)\cos(b)-\sin(b)\cos(a)\]
anonymous
  • anonymous
so would cos u =4/5 for the first one?
freckles
  • freckles
yes
anonymous
  • anonymous
cool :) can you show me how to set up the second one I'm a little confused on how it would look like
freckles
  • freckles
my thing isn't notifying me when people reply \[\sin(a-b)=\sin(a)\cos(b)-\sin(b)\cos(a) \\ \text{ where } a=\arccos(\frac{5}{13}) \text{ and } b=\arccos(\frac{4}{5} ) \\ \text{ so } \cos(a)=\frac{5}{13} \text{ and } \cos(b)=\frac{4}{5}\] find sin(a) and cos(b) in a similar way you did for the previous question

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