Question

Find the exact value of sin (arccos (3/5)). For full credit, explain your reasoning.

Answer 1

So if we have x=arccos(3/5) then cos(x)=3/5.
Draw a right triangle and use cos(x)=3/5 to find the other missing leg.
then evaluate sin(x)

Answer 2

Myininaya has it down, abc. You should follow myininaya's hint.

Answer 3

im sorry i still dont understand it could you explain it more? like is it like pythagorean therom?

Answer 4

Exactly. recall that cosx is just adjacent over the hypotenuse. So, your adj side is 3 and your hypotenuse is 5. Now just find the missing side by applying pythagorean's theorem and then go back and answer your question.

Answer 5

would it be 4/5?

Answer 6

yes
For full credit, explain your reasoning.

Answer 7

I drew a right triangle I used cos(x)=3/5 to find the other missing leg. I know that cosx is just adjacent over the hypotenuse. So, the adj side is 3 and your hypotenuse is 5. I found the missing side by applying pythagorean's theorem and my answer is 4/5

Answer 8

@phi is this a good answer?

Answer 9

yes, sounds good (but I would leave out the "just" in "just adjacent over hypotenuse"
I found the missing side by applying pythagorean's theorem
I would add "and it is 4"

then add the definition of the sin: opposite over adjacent

Answer 10

okay thank you so much everyone for all of your help!!!