Question

Find sin(theta) , if cos(theta)=(4/9) and theta is in the first quadrant

Answer 1

Answer:
`\sin(\theta) = (√(65))/(9)`

Work Shown

`\sin^2(\theta)+\cos^2(\theta) = 1\\\\\sin(\theta) = √(1-\cos^2(\theta)) \ \ \ \text{when } \theta \text{ is in 1st quadrant}\\\\\sin(\theta) = \sqrt{1-\left((4)/(9)\right)^2}\\\\\sin(\theta) = \sqrt{1-(16)/(81)}\\\\`

`\sin(\theta) = \sqrt{(81)/(81)-(16)/(81)}\\\\\sin(\theta) = \sqrt{(81-16)/(81)}\\\\\sin(\theta) = \sqrt{(65)/(81)}\\\\\sin(\theta) = (√(65))/(√(81))\\\\\sin(\theta) = (√(65))/(9)\\\\`