40.8k views
0 votes
If cos a= 1/2, what is tan a?

1 Answer

1 vote

The cosine of an angle can be expressed as,


\begin{gathered} \cos \text{ a=}\frac{\text{adjacent side}}{\text{hypotenuse}} \\ \cos a=(1)/(2) \end{gathered}

From above equation, we can take adjacent side=1 and hypotenuse =2.

Using pythagorus theorem,


\begin{gathered} \text{hypotenuse}^2=oppositeside^2+adjacentside^2 \\ 2^2=oppositeside^2+1^2 \\ 4=oppositeside^2+1^{} \\ 3=oppositeside^2 \\ \sqrt[]{3}=oppositeside^{} \end{gathered}

Now, the tan of a is,


\begin{gathered} \tan a=\frac{opposite\text{ side}}{\text{adjacent side}} \\ \tan a\text{ =}\frac{\sqrt[]{3}}{1} \\ \tan a=\sqrt[]{3} \end{gathered}

METHOD 2

cos a=1/2. cos function has 1/2 as value when a=60 degrees.

So, a=60.


\tan a=\tan 60^(\circ)=\sqrt[]{3}

User Vanya Burduk
by
7.7k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories