Question

cosy − sin y

Answer 1

Given:

Triangle △ QYR

QR = 21 cm (hypotenuse)

RY = 12 (perpendicular)

QY=?

Step 1: Use Pythagoras Theorem in △QYR:

QR² = QY² + RY²

21² = QY² + 12²

441 = QY² = 144

QY2 = 441 − 144 = 297

QY = `sqrt297`

`sqrt297 = sqrt(9 xx 33)`

`QY = sqrt9 xx sqrt33 = 3sqrt33`

Step 2: Use Trigonometric Ratios

`cos y = "adjacent"/"hypotenuse" = (QY)/(QR) = (3sqrt33)/21 = sqrt33/7`

`sin y = "opposite"/"hypotenuse" = RY/QR = 12/21 = 4/7`

`cos y − sin y = sqrt33/7 − 4/7 = (sqrt(33) − 4)/7 `