If cos A = -2/3 and 90˚ < A < 180˚,

Question

find exact value of cot A,tanA, and sinA

Answer 1

cosA = - (2/3)

cosA = adjacent side/Hypotenuse

A is in second quadrant.

From the Pythagorean theorem (hypotenuse)²  = (adjacent side)²  + (opposite side)² 

Opposite side = √[(hypotenuse)² - (adjacent side)²]

= √[(3)² - (2)²]

= √(9 - 4)

= √5

cotA = adjacent side/opposite side

cotA = - (2/√5)

tanA = opposite side/adjacent side

tanA = -(√5/2)

sinA = opposite side/hypotenuse

sinA = √5/3.