Question

Use a cofunction to write an expression a. csc 3/7b. tan /5

Answer 1

a.

`\sec (\pi)/(14)`

b.

`\cot (3\pi)/(10)`

Explanation:

a.

We have that the function of the cosecant trigonometric ratio is secant, where the angle is complemented by 90 degrees which is equal to /2 therefore:

`\begin{gathered} \csc (x)=\sec \mleft((\pi)/(2)-x\mright) \\ \csc \: \mleft((3\pi)/(7)\mright)=\sec \mleft((\pi)/(2)-\: \: \mleft((3\pi)/(7)\mright)\mright)=\sec (\pi)/(14) \end{gathered}`

b.

We have that the function of the tangent trigonometric ratio is cotangent, where the angle is complemented by 90 degrees which is equal to /2 therefore:

`\begin{gathered} \tan (x)=\cot \mleft((\pi)/(2)-x\mright) \\ \tan \: \mleft((\pi)/(5)\mright)=\cot \mleft((\pi)/(2)-\: \: \mleft((\pi)/(5)\mright)\mright)=\cot (3\pi)/(10) \end{gathered}`