Question

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

Answer 1

Hint: Pythagorean Trig Identity
\[\Large \sin^2(x) + \cos^2(x) = 1\]

Answer 2

Ok, so how would I continue off that? May you guide me through the problem please?

Answer 3

since sine is 1/2, squaring that gives you 1/4

you can replace all of sin^2 with 1/4 like this

\[\Large \sin^2(x) + \cos^2(x) = 1\]
\[\Large \frac{1}{4} + \cos^2(x) = 1\]

Answer 4

now isolate cos(x)

Answer 5

we subract 1/4 from both sides

Answer 6

so now we square root both sides right?

Answer 7

correct on both statements

Answer 8

then how do we get tangent

Answer 9

\[\Large \tan(x) = \frac{\sin(x)}{\cos(x)}\]

Answer 10

Ok, hold on. Let me put everything together.

Answer 11

cos(x) = \[\sqrt{.75}\]
is that how it should be written

Answer 12

or \[\Large \sqrt{\frac{3}{4}} = \frac{\sqrt{3}}{\sqrt{4}} = \frac{\sqrt{3}}{2}\]

Answer 13

most books I've seen use \[\Large \frac{\sqrt{3}}{2}\]

Answer 14

oh ok, so \[\tan(x) = \frac{ 1 }{ 2 } /\frac{ \sqrt{3} }{ 2 }\]

Answer 15

Yes correct. Now simplify

Answer 16

How would I do that?