# Find cos a and tan a if sin a = 2 / 3.0 degrees

September 28, 2021 | education

| To solve this problem, recall that the cosine of an angle can be expressed in terms of the sine of an angle using the basic trigonometric identity: ((sin (A)) ^ 2) + ((cos (A)) ^ 2) = 1. Then cos (A) = √ (1- (sin (A)) ^ 2).

Knowing that sin (A) = 2/3, we calculate the cosine.

cos (A) = √1- (2/3) ^ 2 = √1-4 / 9 = √5 / 9 = √5 / 3.

We calculate the tangent, knowing that the tangent of an acute angle is the ratio of the sine of the angle to its cosine.

tg (A) = 2/3: √5 / 3 = 2 * 3 / √5 * 3 = 2 / √5.

Answer: cosine is √5 / 3, tangent is 2 / √5.