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If sin θ = 5/6 , what are the values of cos θ and tan θ? (2 points)



cos θ = ± 11/36; tan θ = ± 1/11


cos θ = ± \(\sqrt{11}/6\) ; tan θ = -1/11


cos θ = ± 11/6; tan θ = -5/11


cos θ = ± \(\sqrt{11}/6\) ; tan θ = ± 5\(\sqrt{11}/6\)

Please can someone help explain step-by-step how to do this? I'm totally lost

Verified Answer :

Answer: \(cos\theta=\pm \sqrt{11} /6\) and \(tan\theta =\pm \frac{5}{\sqrt{11} }\)

Step-by-step explanation:

Since, here \(sin\theta=5/6\)

And we know that \(cos\theta =\sqrt{1-sin^2\theta}\)

So \(cos\theta=\sqrt{1-(5/6)^2} =\sqrt{1-25/36} =\sqrt{11/36} =\pm\frac{\sqrt{11} }{6}\)

Thus, \(cos\theta=\pm\frac{\sqrt{11} }{6}\)

Now, we know that \(tan\theta=sin\theta/cos\theta=\frac{5/6}{\pm \sqrt{11}/6 } =\frac{5}{\pm \sqrt{11} }\)

Thus, \(tan\theta=\frac{5}{\pm \sqrt{11} }\)


abidemiokin

The value of cosθ and tan θ are \(\frac{\pm \sqrt{11} }{6} \ and \ \frac{5}{\sqrt{11}}\)

Trigonometry identity

Given the trigonometry identity sin θ = 5/6

  • Opposite  = 5
  • Hypotenuse = 6

Get the value of the adjacent side

\(adj^2 = 6^2 - 5^2\\ adj^2 = 36 - 25\\ adj^2 = 11\\ adj=\sqrt{11}\)

Get the value of cosθ and tan θ

\(cos \theta = \frac{adj}{hyp} = \frac{\pm\sqrt{11} }{6}\\ tan \theta = \frac{opp}{adj} = \frac{5 }{\sqrt{11} }\)

Hence the value of cosθ and tan θ are \(\frac{\pm \sqrt{11} }{6} \ and \ \frac{5}{\sqrt{11}}\)

Learn more on trigonometry identity: https://brainly.com/question/7331447

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