Respuesta :
Answer:
Hence The other five trigonometric function as :
CosФ =[tex]\frac{\sqrt{73}}{8}[/tex]
TanФ = [tex]\frac{3}{\sqrt{73}}[/tex]
SecФ = [tex]\frac{8}{\sqrt{73}}[/tex]
CotФ =[tex]\frac{\sqrt{73}}{3}[/tex]
Step-by-step explanation:
Given as :
sin Ф = [tex]\frac{3}{8}[/tex]
∵ sin Ф = [tex]\frac{perpendicular}{hypotenuse}[/tex]
So, [tex]\frac{perpendicular}{hypotenuse}[/tex] = [tex]\frac{3}{8}[/tex]
Then from Pythagorean theorem
Hypotenuse² = Perpendicular² + Base²
So, Base² = Hypotenuse² - Perpendicular²
Or, Base² = 8² + 3² = 64 + 9 = 73
∴ Base = √73
So, CosФ = [tex]\frac{Base}{hypotenuse}[/tex]
CosФ = [tex]\frac{\sqrt{73}}{8}[/tex]
TanФ = [tex]\frac{perpendicular}{Base}[/tex]
TanФ = [tex]\frac{3}{\sqrt{73}}[/tex]
SecФ = [tex]\frac{hypotenuse}{base}[/tex]
SecФ = [tex]\frac{8}{\sqrt{73}}[/tex]
CotФ = [tex]\frac{Base}{Perpendicular}[/tex]
CotФ = [tex]\frac{\sqrt{73}}{3}[/tex]
CosecФ = [tex]\frac{hypotenuse}{perpendicular}[/tex]
CosecФ = [tex]\frac{8}{3}[/tex]
Hence The other five trigonometric function as :
CosФ = [tex]\frac{\sqrt{73}}{8}[/tex]
TanФ = [tex]\frac{3}{\sqrt{73}}[/tex]
SecФ = [tex]\frac{8}{\sqrt{73}}[/tex]
CotФ = [tex]\frac{\sqrt{73}}{3}[/tex]
CosecФ = [tex]\frac{8}{3}[/tex] Answer
