Trigonometry
Class 11-12

Sum to Product - Sine

sinA+sinB=2sinA+B2cosAB2\sin A + \sin B = 2\sin\frac{A+B}{2}\cos\frac{A-B}{2}
010203040−2−1.5−1−0.500.511.52
sinA + sinB = 2×sin((A+B)/2)×cos((A-B)/2)

Adjust Variables

Frequency ratio
r =
11.2

Converts sum of sines into a product. Essential for solving equations and analyzing wave interference.

Real-World Applications

Wave beats — Two slightly different frequencies create audible beats.

Radio tuning — Combining signals in radio receivers.

Music — Piano tuning using beat frequencies.

Acoustics — Sound wave interference in concert halls.

Electronics — Signal mixing in communication systems.

Optics — Light interference in thin films.

Sonar — Underwater sound wave combination.

Medical imaging — Ultrasound signal processing.

Seismology — Combining seismic wave data.

Telecommunications — Frequency multiplexing.

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