Given sin A = 3/5, and 0° < A < 90°, find the values of cos A and tan A,?

Question

By using the formula: cos^2 A = 1 - sin^2 A and tan A = sin A / cos A
please explain in detail!
thanks.

Answer 1

sinA = 3 / 5 and 0 < A < pi / 2

Recall : Trigonometry identities sin²A + cos²A = 1 then cos²A = 1 - sin²A

Substitute sinA = 3 / 5 in the above formula

cos²A  = 1 - 9 / 25 = 16 / 25

cosA = 4 / 5  (First quadrant)

 

Answer 2

sinA = 3 / 5 and 0 < A < pi / 2

Recall : Trigonometry identities sin²A + cos²A = 1 then cos²A = 1 - sin²A

Substitute sinA = 3 / 5 in the above formula

cos²A  = 1 - 9 / 25 = 16 / 25

cosA = 4 / 5  (First quadrant)

Recall : Trigonometry identities tanA = sinA / cosA

Substitute sinA = 3 / 5 and cosA = 4 / 5 in the above tanA formula

tanA = (3 / 5) / (4 / 5) = 3 / 4.