Question

How do you do this - with work - using pythagorean identities?

Answer 1

see explanation

Explanation:

Using the trigonometric identities

• 1 + tan²x = sec²x

• cot x =
`(1)/(tanx)`

Given

secΘ =
`(4)/(3)`, then

tan²Θ = sec²Θ - 1 = (
`(4)/(3)` )² - 1 =
`(16)/(9)` - 1 =
`(7)/(9)`, hence

tanΘ = ±
`\sqrt{(7)/(9) }` = ±
`(√(7) )/(3)`

Since 270° < Θ < 360° ← fourth quadrant where tanΘ < 0

Hence tanΘ = -
`(√(7) )/(3)`

and

cotΘ =
`(1)/(-(√(7) )/(3) )` = -
`(3)/(√(7) )` = -
`(3√(7) )/(7)`