If cosine of x equals 1 over 2, what is sin(x) and tan(x)? Explain your steps in complete sentences.

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If cosine of x equals 1 over 2, what is sin(x) and tan(x)? Explain your steps in complete sentences.

Mathematics
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make a right triangle then use cos(x)=1/2 then use Pythagorean theorem to figure out opposite side of x
then you have everything you need to find sin(x) and tan(x)
can u guide me @freckles

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Other answers:

which part do you need help on?
did you draw the right triangle yet?
i guess all.
yes
ok then use cos(x)=1/2 remember cosine, think adjacent/hyp
ok
then use the Pythagorean theorem to find the opp side can you do that?
no
well we know the Pythagorean theorem says: \[opp^2+adj^2=hyp^2 \\ \text{ and we know the } adj \text{ and the hyp } \\ \text{ just solve for opp}\]
adj is 1 and hyp is 2?
yes this was given by cos(x)=1/2 you could also use any thing that reduces down to 1/2 for example cos(x)=10/20 and call the adj=10 and hyp=20 but it doesn't matter in the end we will get the same reduced fractions so yes you can use adj=1 and hyp=2
ok
have you solved for opp yet?
if you have you can find sin(x) and tan(x)
still working on it
opp is root 5?
\[oop^2+1^2=2^2 \\ oop^2+1=4\] 4-1 isn't 5 should be 3
\[opp^2=4-1 \\ opp^2=3 \\ opp= \pm \sqrt{3}\]
shoot my bad
so you have two answers for both sin(x) and tan(x) because of the plus or minus thing
anyways recall sin(x)=opp/hyp and tan(x)=opp/adj
ok
sin(x) = 3/2 tan(x) = 3/1 = 3
what happen to the sqrt( ) part ?
also you should have two answers for each
\[\sin(x)=\frac{ \pm \sqrt{3}}{2} \text{ this is the two answers for } \sin(x) \] now you try tan(x)=?
ok
┬▒root 3?
yep sounds great
how did you get the root sighn tho
sign
jk never mind
\[opp^2+adj^2=hyp^2 \\ opp^2+1^2=2^2 \\ opp^2=4-1 \\ opp^2=3 \\ \text{ \to solve an equation like this you take square root of both sides }\]
but it will also mean you wind up with two possibilities since sqrt(opp^2)=|opp|=opp if opp>0 but =-opp if opp<0
ok. Thank You so so so so much!!!!!!!!!!!!!!!!!!!

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