Answer:
The value of SecФ is [tex]\pm \sqrt{\frac{11}{8}}[/tex] .
Step-by-step explanation:
Given as for trigonometric function :
tan²Ф = [tex]\frac{3}{8}[/tex]
Or, tanФ = [tex]\sqrt{\frac{3}{8} }[/tex]
∵ tanФ = [tex]\frac{Perpendicular}{Base}[/tex]
So, [tex]\frac{Perpendicular}{Base}[/tex] = [tex]\sqrt{\frac{3}{8} }[/tex]
So, Hypotenuse² = perpendicular² + base²
or, Hypotenuse² = ( [tex]\sqrt{3}[/tex] )² + ( [tex]\sqrt{8}[/tex] )²
Or, Hypotenuse² = 3 + 8 = 11
Or, Hypotenuse = ( [tex]\sqrt{11}[/tex] )
Now SecФ = [tex]\frac{Hypotenuse}{Base}[/tex]
or, SecФ = [tex]\frac{\sqrt{11}}{\sqrt{8}}[/tex] = [tex]\sqrt{\frac{11}{8} }[/tex]
Second Method
Sec²Ф - tan²Ф = 1
Or, Sec²Ф = 1 + tan²Ф
or, Sec²Ф = 1 + [tex]\frac{3}{8}[/tex]
Or, Sec²Ф = [tex]\frac{11}{8}[/tex]
Or, SecФ = [tex]\pm \sqrt{\frac{11}{8}}[/tex]
Hence The value of SecФ is [tex]\pm \sqrt{\frac{11}{8}}[/tex] . Answer
