Question

Find cosα given that sinα = 5/13 and α is in quadrant II

Answer 1

cos α = -
`(12)/(13)`

Explanation:

Since α is in second quadrant then cosα < 0

Using the identity

sin²α + cos²α = 1 then

cosα = -
`√(1-sin^2\alpha )`

= -
`\sqrt{1-((5)/(13))^2 }`

= -
`\sqrt{1-(25)/(169) }`

= -
`\sqrt{(144)/(169) }`

= -
`(12)/(13)`