If cosb =sqrt 5 /3?

Question

and angle B is in quadrant I, find sinB

Answer 1

I'll show you how to solve this problem without using a calculator. You won't always have a calculator with you 24/7 in life, and it's important not to develop a reliance of calculators.

cosB = √[5] / 3

cosine = adjacent side / hypotenuse

adjacent side = a = √[5]

hypotenuse = c = 3

opposite side = b = ???

(So we have cosB = a / c, and we want to find sinB, which equals b / c)

Pythagorean Theorem states:

a² + b² = c²

(5) + b² = (9)

b² = 9 - 5

b² = 4

b = 2

b is our opposite side, and since sine = opposite side / hypotenuse, then

sinB = b / c

sin B = 2/3

Answer 2

sqrt 5 /3 = 0.7453559

cos b = 0.7453559

b = 41.81 degrees

sin (41.81) = 0.6666666666667
.