anonymous
  • anonymous
If cosine of x equals 1 over 2, what is sin(x) and tan(x)? Explain your steps in complete sentences.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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freckles
  • freckles
make a right triangle then use cos(x)=1/2 then use Pythagorean theorem to figure out opposite side of x
freckles
  • freckles
then you have everything you need to find sin(x) and tan(x)
anonymous
  • anonymous
can u guide me @freckles

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freckles
  • freckles
which part do you need help on?
freckles
  • freckles
did you draw the right triangle yet?
anonymous
  • anonymous
i guess all.
anonymous
  • anonymous
yes
freckles
  • freckles
ok then use cos(x)=1/2 remember cosine, think adjacent/hyp
anonymous
  • anonymous
ok
freckles
  • freckles
then use the Pythagorean theorem to find the opp side can you do that?
anonymous
  • anonymous
no
freckles
  • freckles
well we know the Pythagorean theorem says: \[opp^2+adj^2=hyp^2 \\ \text{ and we know the } adj \text{ and the hyp } \\ \text{ just solve for opp}\]
anonymous
  • anonymous
adj is 1 and hyp is 2?
freckles
  • freckles
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
anonymous
  • anonymous
ok
freckles
  • freckles
have you solved for opp yet?
freckles
  • freckles
if you have you can find sin(x) and tan(x)
anonymous
  • anonymous
still working on it
anonymous
  • anonymous
opp is root 5?
freckles
  • freckles
\[oop^2+1^2=2^2 \\ oop^2+1=4\] 4-1 isn't 5 should be 3
freckles
  • freckles
\[opp^2=4-1 \\ opp^2=3 \\ opp= \pm \sqrt{3}\]
anonymous
  • anonymous
shoot my bad
freckles
  • freckles
so you have two answers for both sin(x) and tan(x) because of the plus or minus thing
freckles
  • freckles
anyways recall sin(x)=opp/hyp and tan(x)=opp/adj
anonymous
  • anonymous
ok
anonymous
  • anonymous
sin(x) = 3/2 tan(x) = 3/1 = 3
anonymous
  • anonymous
@freckles
freckles
  • freckles
what happen to the sqrt( ) part ?
freckles
  • freckles
also you should have two answers for each
freckles
  • freckles
\[\sin(x)=\frac{ \pm \sqrt{3}}{2} \text{ this is the two answers for } \sin(x) \] now you try tan(x)=?
anonymous
  • anonymous
ok
anonymous
  • anonymous
┬▒root 3?
freckles
  • freckles
yep sounds great
anonymous
  • anonymous
how did you get the root sighn tho
anonymous
  • anonymous
sign
anonymous
  • anonymous
jk never mind
freckles
  • freckles
\[opp^2+adj^2=hyp^2 \\ opp^2+1^2=2^2 \\ opp^2=4-1 \\ opp^2=3 \\ \text{ \to solve an equation like this you take square root of both sides }\]
freckles
  • freckles
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
anonymous
  • anonymous
ok. Thank You so so so so much!!!!!!!!!!!!!!!!!!!

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