If sin θ = 3/8 and θ is in the second quadrant, find values of all 5 other trigonometric functions of θ

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