+0  
 
0
367
4
avatar

if cos(x)=1/2, how do i find sin and tan?

Guest Apr 7, 2017

Best Answer 

 #1
avatar+5548 
+3

Here is a drawing of what cos(x)= 1/2 really means:

 

 

We can find sin(x) just using the Pythagorean Theorem.

 

\((\frac12)^2+(\sin (x))^2=1^2 \\~\\ \mathbf{sin(x)}=\sqrt{1-\frac14}=\sqrt{\frac34}\mathbf{=\frac{\sqrt3}{2}}\)

 

 

tan = sin / cos, so...

 

tan(x) = sin(x) / cos(x) = \(\frac{\sqrt3}{2}\div\frac{1}{2}=\frac{\sqrt3}{2}\cdot\frac{2}{1}\mathbf{=\sqrt3}\)

hectictar  Apr 8, 2017
edited by hectictar  Apr 8, 2017
Sort: 

4+0 Answers

 #1
avatar+5548 
+3
Best Answer

Here is a drawing of what cos(x)= 1/2 really means:

 

 

We can find sin(x) just using the Pythagorean Theorem.

 

\((\frac12)^2+(\sin (x))^2=1^2 \\~\\ \mathbf{sin(x)}=\sqrt{1-\frac14}=\sqrt{\frac34}\mathbf{=\frac{\sqrt3}{2}}\)

 

 

tan = sin / cos, so...

 

tan(x) = sin(x) / cos(x) = \(\frac{\sqrt3}{2}\div\frac{1}{2}=\frac{\sqrt3}{2}\cdot\frac{2}{1}\mathbf{=\sqrt3}\)

hectictar  Apr 8, 2017
edited by hectictar  Apr 8, 2017
 #2
avatar+79716 
+2

cos    = x / r      sin  = y / r   and tan  = y / x

 

We know x and r and we need to find y =  sqrt (r^2 - x^2)  = sqrt (2^2 - 1^2) =

sqrt (4 - 1)   =  sqrt (3)

 

So

 

sin (x)  = y/r =  sqrt (3) / 2       and tan (x) = y/x   =  sqrt (3)  / 1  = sqrt (3)

 

 

cool cool cool 

CPhill  Apr 8, 2017
 #3
avatar+1222 
0

sqrt3

tertre  Apr 8, 2017
 #4
avatar+310 
+2

You forgot a solution. If cos(x)=1/2 then sin(x)=(3/4)1/2 OR sin(x)=-(3/4)1/2

 

That means tan(x)=-(31/2) OR tan(x)=31/2

Ehrlich  Apr 8, 2017

24 Online Users

avatar
We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details