If sin A = 4/5, what is the value of tan A?

If sin A = 4/5, what is the value of tan A?

Step 1: We know that sin A = 4/5.
Step 2: We need to find cos A. We can use the Pythagorean identity: sin^2 A + cos^2 A = 1.
Step 3: Calculate sin^2 A: (4/5)^2 = 16/25.
Step 4: Substitute sin^2 A into the identity: 16/25 + cos^2 A = 1.
Step 5: To find cos^2 A, subtract 16/25 from 1: cos^2 A = 1 - 16/25 = 25/25 - 16/25 = 9/25.
Step 6: Take the square root of cos^2 A to find cos A: cos A = √(9/25) = 3/5.
Step 7: Now we can find tan A using the identity tan A = sin A / cos A.
Step 8: Substitute the values: tan A = (4/5) / (3/5).
Step 9: Simplify the fraction: tan A = 4/5 * 5/3 = 4/3.

Trigonometric Ratios – Understanding the relationships between sine, cosine, and tangent functions.
Pythagorean Identity – Using the identity sin²A + cos²A = 1 to find the cosine value from the sine value.