Question

- Use the unit circle to evaluate
the six trigonometric functions
of theta= 4pi

Answer 1

The six trigonometric functions,
`\sin (\pi)/(4) =(1)/(√(2))`,
`\cos (\pi)/(4) =(1)/(√(2))`,
`\tan (\pi)/(4) =1`,
`\cot (\pi)/(4) =1`,
`\sec (\pi)/(4) =√(2)` and
`\csc (\pi)/(4) =√(2)`.

Explanation:

We have,

`(\pi)/(4)`

To write the six trigonometric functions = ?

`\sin (\pi)/(4) =(1)/(√(2))`

`\cos (\pi)/(4) =(1)/(√(2))`

`\tan (\pi)/(4) =1`

`\cot (\pi)/(4) =1`

`\sec (\pi)/(4) =√(2)`

`\csc (\pi)/(4) =√(2)`

∴ The six trigonometric functions,
`\sin (\pi)/(4) =(1)/(√(2))`,
`\cos (\pi)/(4) =(1)/(√(2))`,
`\tan (\pi)/(4) =1`,
`\cot (\pi)/(4) =1`,
`\sec (\pi)/(4) =√(2)` and
`\csc (\pi)/(4) =√(2)`.