Question

If cos a= 1/2, what is tan a?

Answer 1

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}`