Sum Difference Formulas Worksheets Grade 12

1. Liam is designing a suspension bridge where the main cable follows the curve y = 50sin(0.02x) + 100cos(0.02x). To analyze the stress distribution, he needs to rewrite this function in the form y = Rsin(0.02x + α). Using sum and difference formulas, determine the amplitude R of the cable's oscillation.
2. Emma is designing a triangular garden with sides forming angles of 13°, 37°, and 130° with the north direction. The garden is inscribed in a circular pond with radius 7 meters. Using sum and difference formulas for trigonometric functions, find the exact length of the side opposite the 130° angle.
3. Mason is a civil engineer analyzing the voltage output of a solar panel array. The instantaneous voltage is given by V(t) = 24 sin(120πt + 7π/12) volts. To verify a reading at a specific time, Mason needs to compute the exact voltage at t = 1/240 seconds using the sum formula for sine. What is the exact value of V(1/240) in simplest radical form?

…and 2 more problems

1. cos(55°)cos(25°) + sin(55°)sin(25°) = ?
2. Noah is an acoustical engineer analyzing sound wave interference patterns. Two sound waves combine to produce a resultant wave described by the function y = 6 sin(2x) - 8 cos(2x). To determine the maximum amplitude of the combined wave, Noah needs to rewrite this expression in the form y = R sin(2x - φ) using sum and difference formulas. What is the amplitude R of the combined wave?
3. An engineer is designing a roller coaster track that follows the path y = 12sin(x) + 5cos(x) meters, where x is the horizontal distance from the starting point. To determine the maximum height of the track, she needs to rewrite this function in the form y = Rsin(x + φ) using sum and difference formulas. What is the amplitude R of the simplified sinusoidal function?

…and 4 more problems

1. An engineer is designing a roller coaster track that follows the path y = 12sin(x) + 5cos(x) meters. To analyze the maximum height of the track, she needs to rewrite this function in the form y = Rsin(x + α) using sum and difference formulas. What is the amplitude R of the simplified sinusoidal function?
2. sin(40°)cos(20°) + cos(40°)sin(20°) = ?
3. An engineer is designing a roller coaster track that follows the path y = 12sin(x) + 5cos(x) meters, where x is the horizontal distance from the start. To determine the maximum height of the track, she needs to rewrite this function in the form y = Rsin(x + α) using sum and difference formulas. What is the amplitude R of the simplified sinusoidal function?

…and 5 more problems