If sin(θ) = 4/5, what is the value of tan(θ)?

If sin(θ) = 4/5, what is the value of tan(θ)?

Step 1: We know that sin(θ) = 4/5.
Step 2: We need to find cos(θ) using the identity cos(θ) = √(1 - sin^2(θ)).
Step 3: First, calculate sin^2(θ): (4/5)² = 16/25.
Step 4: Now, substitute sin^2(θ) into the cos(θ) formula: cos(θ) = √(1 - 16/25).
Step 5: Simplify inside the square root: 1 - 16/25 = 25/25 - 16/25 = 9/25.
Step 6: Now, take the square root: cos(θ) = √(9/25) = 3/5.
Step 7: Now we have sin(θ) = 4/5 and cos(θ) = 3/5.
Step 8: Use the identity tan(θ) = sin(θ)/cos(θ) to find tan(θ).
Step 9: Substitute the values: tan(θ) = (4/5) / (3/5).
Step 10: Simplify the fraction: tan(θ) = 4/5 * 5/3 = 4/3.

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