Question

Find θ to four significant digits for 0< θ<2 π if tan θ= -0.3573

Answer 1

Given:

`tan\theta=-0.3573`

Aim:

`We\text{ need to find the value of }\theta.`

Step-by-step explanation:

`tan\theta=-0.3573`

Taking inverse trigonometry on both sides.

`tan^(-1)tan\theta=tan^(-1)(-0.3573)`

`\theta=tan^(-1)(-0.3573)`
`\theta=-19.6618087737`
`\theta\approx-19.6618`

We know that

`tan(180+\theta)=tan\theta`
`tan(180-19.6618)=tan(-19.6618)`

`tan(160.3382)=tan(-19.6618)`

The angels are

`-19.6618\text{ and 160.3382}`

Final answer:

`\theta=19.6618,160.3382`