Question

Given that tan^2 theta=3/8,what is the value of sec theta?

Answer 1

b

Explanation:

Answer 2

The value of SecФ is
`\pm \sqrt{(11)/(8)}` .

Explanation:

Given as for trigonometric function :

tan²Ф =
`(3)/(8)`

Or, tanФ =
`\sqrt{(3)/(8) }`

∵ tanФ =
`(Perpendicular)/(Base)`

So,
`(Perpendicular)/(Base)` =
`\sqrt{(3)/(8) }`

So, Hypotenuse² = perpendicular² + base²

or, Hypotenuse² = (
`√(3)` )² + (
`√(8)` )²

Or, Hypotenuse² = 3 + 8 = 11

Or, Hypotenuse = (
`√(11)` )

Now SecФ =
`(Hypotenuse)/(Base)`

or, SecФ =
`(√(11))/(√(8))` =
`\sqrt{(11)/(8) }`

Second Method

Sec²Ф - tan²Ф = 1

Or, Sec²Ф = 1 + tan²Ф

or, Sec²Ф = 1 +
`(3)/(8)`

Or, Sec²Ф =
`(11)/(8)`

Or, SecФ =
`\pm \sqrt{(11)/(8)}`

Hence The value of SecФ is
`\pm \sqrt{(11)/(8)}` . Answer