Question

Find the exact value of cos(arcsin(one fourth)). For full credit, explain your reasoning.

Answer 1

\[\theta = \sin^{-1} (1/4)\]
which means
\[\sin \theta = \frac{1}{4}\]
you have to find cos theta
pythagorean identity is:
\[\sin^{2} \theta + \cos^{2} \theta = 1\]
\[\frac{1}{16} + \cos^{2} \theta = 1\]
\[\cos \theta = \pm \sqrt{1-\frac{1}{16}}\]

Answer 2

@dumbcow doesn't the answer need to be something like pi/4 or 2pi/3 ?

Answer 3

hmm no because they are not asking for the angle but the cos of the angle "arcsin 1/4"

Answer 4

@dumbcow well all of my other questions have had an answer like that.so i just thought this one needed an answer like that also.

Answer 5

sin(x) gives a ratio between -1 and 1

arcsin(x) gives an angle (usually in terms of pi)

so the type of answer depends on the question and what you are asked to find

Answer 6

the question is "Find the exact value of cos(arcsin(one fourth)). For full credit, explain your reasoning." but the multiple choice questions before all had answers like pi/4 or pi/3 and they said the same thing

Answer 7

are you sure it was exactly the same thing

here is solution from wolfram
http://www.wolframalpha.com/input/?i=cos%28arcsin%281%2F4%29%29

Answer 8

there is an angle with \(\sin(\theta)=\frac{1}{4}\)
adjacent side is , via pythagoras, \(\sqrt{4^2-1^2}=\sqrt{15}\)

Answer 9

@dumbcow yes i am sure, do you think you can help me out with the answer that relates to that?

Answer 10

this tells you
\[\cos(\theta)=\frac{\sqrt{15}}{4}\]

Answer 11

triangle approach works great too
thanks @satellite73

Answer 12

either way, i think the picture is easiest, but it all comes down to pythagoras in any case
amazing how much mileage comes out of that little theorem

Answer 13

alright, thank. @satellite73 @dumbcow

Answer 14

yw, if your multiple choice answers all are angles then your teacher had a typo :{