Question

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))

Answer 1

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

Answer 2

that one thing is suppose to be u

Answer 3

the second one I would expand and make two right triangles

Answer 4

expand using:
\[\sin(a-b)=\sin(a)\cos(b)-\sin(b)\cos(a)\]

Answer 5

so would cos u =4/5 for the first one?

Answer 6

yes

Answer 7

cool :) can you show me how to set up the second one I'm a little confused on how it would look like

Answer 8

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