Question

How is this worked out ? im confused.

Answer 1

From the given ratio for
`tan\theta=(4)/(5)` we found the values are

`sin\theta=4`

`cos\theta=5`

`csc\theta=(1)/(4)`

`sec\theta=(1)/(5)`

`cot\theta=(5)/(4)}`

Explanation:

Given the ratio for
`tan\theta=(4)/(5)`

We have to find the rest of trignometric functions:

`tan\theta=(4)/(5)\hfill (1)`

`tan\theta` can be written as

`tan\theta=(sin\theta)/(cos\theta)\hfill (2)`

Comparing equations (1) and (2) we get

`tan\theta=(sin\theta)/(cos\theta)=(4)/(5)`

`(sin\theta)/(cos\theta)=(4)/(5)`

Equating the coressponding numerator and denominator respectively

Therefore
`sin\theta=4` and
`cos\theta=5`

We can find
`csc\theta`

`csc\theta=(1)/(sin\theta)`

`=(1)/(4)` (since
`sin\theta=4`)

`csc\theta=(1)/(4)`

We can find
`sec\theta`

`sec\theta=(1)/(cos\theta)`

`=(1)/(5)` (since
`cos\theta=5`)

`sec\theta=(1)/(5)`

To find
`cot\theta`:

`cot\theta=(1)/(tan\theta)`

`=(1)/((4)/(5))`

`=1* (5)/(4)`

`=(5)/(4)}`

`cot\theta=(5)/(4)}`