Half-Angle Calculator

Compute sin(θ/2), cos(θ/2) or tan(θ/2) using their half-angle identities.

Step-by-step method

1. Identify what is given.
2. Write the correct half-angle identity.
3. Substitute the values and calculate.

Formulas:

Formula: sin(θ/2)

Formula: cos(θ/2)

Formula: tan(θ/2)

Example 1: sin(θ/2) with θ = 60°

Step 1 - Identify what is given.

In this problem: The given angle is θ = 60°.

Step 2 - Write the correct half-angle identity.

In this problem: Use the identity: sin(θ/2) = √((1 − cosθ) / 2).

Step 3 - Substitute the values and calculate.

In this problem: First find cosθ = cos(60°) = 0.5, then substitute and compute.

Final answer: sin(θ/2) = 0.5

Example 2: tan(θ/2) with θ = 30°

Step 1 - Identify what is given.

In this problem: The given angle is θ = 30°.

Step 2 - Write the correct half-angle identity.

In this problem: Use the identity: tan(θ/2) = √((1 − cosθ) / (1 + cosθ)).

Step 3 - Substitute the values and calculate.

In this problem: First find cosθ = cos(30°) = 0.8660254, then substitute and compute.

Final answer: tan(θ/2) = 0.26794919