If sin A = 0.8, what is the value of tan A?

If sin A = 0.8, what is the value of tan A?

Step 1: Start with the given value, sin A = 0.8.
Step 2: Use the identity for tangent, which is tan A = sin A / cos A.
Step 3: To find cos A, use the formula cos A = √(1 - sin² A).
Step 4: Calculate sin² A, which is 0.8 * 0.8 = 0.64.
Step 5: Substitute sin² A into the formula: cos A = √(1 - 0.64).
Step 6: Calculate 1 - 0.64, which equals 0.36.
Step 7: Now find cos A: cos A = √(0.36) = 0.6.
Step 8: Now that we have both sin A and cos A, substitute them into the tangent formula: tan A = 0.8 / 0.6.
Step 9: Calculate 0.8 divided by 0.6, which equals approximately 1.3333.
Step 10: Round the answer to one decimal place, which is approximately 1.3.

Trigonometric Identities – Understanding the relationship between sine, cosine, and tangent functions.
Pythagorean Identity – Using the identity sin² A + cos² A = 1 to find cosine from sine.