Question

find the exact value of sin(cos^-1(3/7)).
a. undefined
b. (2sqrt10)/7
c. 40/49
d. 7/(2sqrt10)

Answer 1

hmm let call \[\arccos(\frac{3}{7})=\theta\]
so \[\cos\theta=\frac{3}{7}\]
we can draw a picture that can help us here

Answer 2

we need to find ?
we can use pythagorean theorem
\[x^2+3^2=7^2 \Longrightarrow x=\sqrt{49-9}=2\sqrt{10}\]

Answer 3

x is the missing side we found it

Answer 4

now we do \[\sin \theta\] which is the same as \[\sin (\arccos(\frac{3}{7}))\]

Answer 5

i let you do this part...

Answer 6

from the triangle what is sin theta

Answer 7

I got .903

Answer 8

remember sin is opp/hyp

Answer 9

which would be b correct

Answer 10

sin=opp/hyp like @magepker728
the opposite is \[2\sqrt{10}\]
the hyp=7

Answer 11

i guess you are not interested lol