Respuesta :
[tex]\sin \theta=\dfrac{p}{h} =\dfrac{-7}{\sqrt{85} }[/tex], [tex]\cos \theta=\dfrac{b}{h} =\dfrac{6}{\sqrt{85}}[/tex], [tex]\tan \theta=\dfrac{p}{b} =\dfrac{-7}{6}[/tex],
[tex]\sec \theta=\dfrac{h}{b} =\dfrac{\sqrt{85} }{6}[/tex] and [tex]\csc \theta=\dfrac{h}{p} =\dfrac{-\sqrt{85}}{ 7}[/tex]
Explanation:
Given,
[tex]\cot \theta= \dfrac{-6}{7}[/tex]
To find, the exact values of the five remaining trigonometric functions of [tex]\theta[/tex] = ?
We know that,
[tex]\cot \theta= \dfrac{-6}{7}=\dfrac{b}{p}[/tex]
Where, b = base and p = perpendicular
By Pythagoras's theorem,
Hypotaneous, [tex]h=\sqrt{p^2+b^2}[/tex]
[tex]=\sqrt{(-6)^2+7^2}=\sqrt{36+49} =\sqrt{85}[/tex]
In IVth quadrant,
[tex]\cot \theta[/tex] and [tex]\sec \theta[/tex] are positive.
[tex]\sin \theta=\dfrac{p}{h} =\dfrac{-7}{\sqrt{85} }[/tex], [tex]\cos \theta=\dfrac{b}{h} =\dfrac{6}{\sqrt{85}}[/tex], [tex]\tan \theta=\dfrac{p}{b} =\dfrac{-7}{6}[/tex],
[tex]\sec \theta=\dfrac{h}{b} =\dfrac{\sqrt{85} }{6}[/tex] and [tex]\csc \theta=\dfrac{h}{p} =\dfrac{-\sqrt{85}}{ 7}[/tex]
