Question

How do I solve this, sin to cot answer in fraction or integer?

Answer 1

The slope of the given equation is

`m=-(A)/(B)`

Where A = 2, and B = 1.

`m=-(2)/(1)=-2`

But, the slope is equal to the tangent function:

`\begin{gathered} \tan \theta=m=-(2)/(1) \\ \end{gathered}`

If we consider this tangent function about a right triangle, then the opposite leg is 2, and the adjacent leg is 1. Using Pythagorean's Theorem, we find the hypothenuse.

`\begin{gathered} h^2=2^2+1^2 \\ h=\sqrt[]{4+1} \\ h=\sqrt[]{5} \end{gathered}`

So, the sine function is

`\sin \theta=\frac{2}{\sqrt[]{5}}\approx0.89`

And, the cosine function is

`\cos \theta=\frac{1}{\sqrt[]{5}}\approx0.45`

The inverses are

`\begin{gathered} \cot =(1)/(2) \\ \sec =\frac{\sqrt[]{5}}{1}\approx2.23 \\ \csc =\frac{\sqrt[]{5}}{2}\approx1.12 \end{gathered}`