Answer: [tex]cos\theta=\pm \sqrt{11} /6[/tex] and [tex]tan\theta =\pm \frac{5}{\sqrt{11} }[/tex]
Step-by-step explanation:
Since, here [tex]sin\theta=5/6[/tex]
And we know that [tex]cos\theta =\sqrt{1-sin^2\theta}[/tex]
So [tex]cos\theta=\sqrt{1-(5/6)^2} =\sqrt{1-25/36} =\sqrt{11/36} =\pm\frac{\sqrt{11} }{6}[/tex]
Thus, [tex]cos\theta=\pm\frac{\sqrt{11} }{6}[/tex]
Now, we know that [tex]tan\theta=sin\theta/cos\theta=\frac{5/6}{\pm \sqrt{11}/6 } =\frac{5}{\pm \sqrt{11} }[/tex]
Thus, [tex]tan\theta=\frac{5}{\pm \sqrt{11} }[/tex]
The value of cosθ and tan θ are [tex]\frac{\pm \sqrt{11} }{6} \ and \ \frac{5}{\sqrt{11}} [/tex]
Given the trigonometry identity sin θ = 5/6
Get the value of the adjacent side
[tex]adj^2 = 6^2 - 5^2\\ adj^2 = 36 - 25\\ adj^2 = 11\\ adj=\sqrt{11} [/tex]
Get the value of cosθ and tan θ
[tex]cos \theta = \frac{adj}{hyp} = \frac{\pm\sqrt{11} }{6}\\ tan \theta = \frac{opp}{adj} = \frac{5 }{\sqrt{11} }[/tex]
Hence the value of cosθ and tan θ are [tex]\frac{\pm \sqrt{11} }{6} \ and \ \frac{5}{\sqrt{11}} [/tex]
Learn more on trigonometry identity: https://brainly.com/question/7331447
