Double Angle Calculator Guide

The tool is a static browser calculator powered by JavaScript. It reads angle θ, converts to radians internally, and evaluates sin(2θ), cos(2θ), and tan(2θ) using standard library math functions. No data is sent to a server.

There is no function selector because all three outputs display at once. That matches how most textbook exercises ask you to find more than one ratio at the same angle. You enter θ once and read three rows.

Degree and radian support covers typical textbook notation. The third mode, π rad, treats your input as a multiple of π. Enter 0.5 for π/2 radians or 0.333333 for π/3. This mode saves typing when problems are written in terms of π.

When tan(2θ) is undefined, the calculator shows a placeholder rather than a misleading large number. That happens at odd multiples of 90° in degree mode, for example, when cos(2θ) = 0 in the tangent ratio.

Results follow standard identities:

• Sine of angle 2θ = sin(2θ) = 2 sin θ cos θ
• Cosine of angle 2θ = cos(2θ)
• Tangent of angle 2θ = tan(2θ) = sin(2θ) / cos(2θ) when cos(2θ) ≠ 0

The labels on the panel name the function and the angle 2θ explicitly so you do not confuse them with values at θ alone. If you need a refresher on each identity form, the Double Angle Formula article lists all variants with usage notes.

1. Open the calculator. Go to /#calculator on the homepage. The panel sits directly below the hero section.
2. Enter θ in the angle field. Type the numeric value. For π/6 in π rad mode, enter approximately 0.166667.
3. Select deg, rad, or π rad. Match the unit your problem uses. Switching units after entry updates all three results instantly.
4. Read the three result rows. Compare sine, cosine, and tangent at 2θ against your handwritten work.
5. Cross-check with examples. Compare with manual work from Double Angle Examples when learning a new angle or unit mode.

Example 1: degrees: Enter θ = 45 with deg selected.

sin(90°) = 1, cos(90°) = 0, tan(90°) is undefined. The calculator reflects the undefined tangent correctly.

Example 2: radians: Enter θ = 1.047197551 (approximately π/3) with rad selected.

2θ ≈ 2.094395 rad (2π/3). You should see sin(2θ) = √3/2, cos(2θ) = −1/2, and tan(2θ) = −√3.

Example 3: π rad mode: Enter 0.25 for θ = π/4.

Results match sin(π/2) = 1, cos(π/2) = 0, with tangent again undefined. Try the same θ in each unit mode to build intuition for conversions.