Question

If sin Θ = 5/6 , what are the values of cos Θ and tan Θ?

Answer 1

Answer: The required values are

`\cos\theta=\pm(√(11))/(6),\\\\\\\tan\theta=\pm(5√(11))/(11).`

Step-by-step explanation: We are given the following value :

`\sin\theta=(5)/(6)`

We are to find the values of
`\cos\theta` and
`\tan\theta.`

We will be using the following formulas :

`(i)\sin^2x+\cos^2x=1,\\\\\\(ii)\tan x=(\sin x)/(\cos x).`

We have

`\cos\theta\\\\\\=\pm√(1-\sin^2\theta)\\\\\\=\pm\sqrt{1-(25)/(36)}\\\\\\=\pm\sqrt{(11)/(36)}\\\\\\=\pm(√(11))/(6)`

and

`\tan\theta=(\sin\theta)/(\cos\theta)=((5)/(6))/(\pm(√(11))/(6))=\pm(5)/(√(11))=\pm(5√(11))/(11).`

Thus, the required values are

`\cos\theta=\pm(√(11))/(6),\\\\\\\tan\theta=\pm(5√(11))/(11).`

Answer 2

For the answer to the question above, I'll provide a solution to my answer below
sin²θ + cos²θ = 1

so, cos²θ = 1 - (5/6)² => 11/36

=> cosθ = ±√11/6

Also, tanθ = sinθ/cosθ => (5/6)/(±√11/6)

i.e. tanθ = ±5/√11
I hope my answer helped you. Feel free to ask more questions. Have a nice day!