Question

MULTIPLE CHOICE, PLS HELP!!

θ lies in Quadrant II .

sinθ=4/7

What is the exact value of cosθ in simplified form?

Answer 1

We know that : Sin²θ + Cos²θ = 1

Given : Sinθ
`\bf{= (4)/(7)}`

`\bf{\implies ((4)/(7))^2 + Cos^2(\theta) = 1}`

`\bf{\implies Cos^2(\theta) = 1 - (16)/(49)}`

`\bf{\implies Cos^2(\theta) =((49 - 16)/(49))}`

`\bf{\implies Cos^2(\theta) =((33)/(49))}`

`\bf{\implies Cos(\theta) = (\pm)((√(33))/(7))}`

Given : θ lies in Quadrant II

We know that : Cosθ is Negative in Quadrant II

`\bf{\implies Cos(\theta) = (-)((√(33))/(7))}`

Option 3 is the Answer