Question

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

Answer 1

Answer:

b

Step-by-step explanation:

Answer 2

Answer:

The value of SecФ is  $\pm \sqrt{\frac{11}{8}}$ .

Step-by-step explanation:

Given as for trigonometric function :

tan²Ф = $\frac{3}{8}$

Or, tanФ = $\sqrt{\frac{3}{8} }$

∵ tanФ = $\frac{Perpendicular}{Base}$

So,  $\frac{Perpendicular}{Base}$ =  $\sqrt{\frac{3}{8} }$

So, Hypotenuse² = perpendicular² + base²

or, Hypotenuse² = ( $\sqrt{3}$ )² + ( $\sqrt{8}$ )²

Or,  Hypotenuse² = 3 + 8 = 11

Or,  Hypotenuse = ( $\sqrt{11}$ )

Now SecФ = $\frac{Hypotenuse}{Base}$

or, SecФ = $\frac{\sqrt{11}}{\sqrt{8}}$ = $\sqrt{\frac{11}{8} }$

Second Method

Sec²Ф - tan²Ф = 1

Or, Sec²Ф = 1 +  tan²Ф

or, Sec²Ф = 1 +  $\frac{3}{8}$

Or, Sec²Ф = $\frac{11}{8}$

Or,  SecФ = $\pm \sqrt{\frac{11}{8}}$

Hence The value of SecФ is  $\pm \sqrt{\frac{11}{8}}$ . Answer