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NikAS [45]
3 years ago
9

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

Mathematics
2 answers:
algol [13]3 years ago
7 0

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} }

<u>Second Method</u>

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

ValentinkaMS [17]3 years ago
7 0

Answer:

b

Step-by-step explanation:

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