When a key is pressed on a touch-tone telephone, the keypad generates two pure tones, which combine to produce a sound that uniquely identifies the key. The figure shows the low frequency f1 and the high frequency f2 associated with each key. Pressing a key produces the sound wave y = sin(2rf3t) + sin(2rf2t). High frequency f2 1209 1336 1477 Hz 697 Hz 2 3 Low 770 Hz - 6. frequency 852 Hz - 8. 9. 941 Hz (a) Find the function that models the sound produced when the 9 key is pressed. y = sin(1704rt) + sin( 2954rt) (b) Use a Sum-to-Product Formula to express the sound generated by the 9 key as a product of a sine and a cosine function. y =

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Fundamentals of Trigonometric Identities

Trigonometric Identities are the equalities that involve trigonometry functions and hold for all the values of variables given in the equation.