Addition Formulas Worksheets Grade 11

1. Hana is a marine biologist studying wave patterns. She models the height of a wave (in meters) over time using the function h(t) = 5 sin(2t + 15°) where t is time in seconds. To analyze the wave's behavior, she needs to rewrite this as a sum of sine and cosine functions. Use the angle addition formula for sine to express h(t) in the form A sin(2t) + B cos(2t), then determine the exact values of A and B.
2. Sophia is an aerospace engineer designing a satellite orbit. She needs to calculate the exact altitude of the satellite at a specific point where the angle from the Earth's center is 105°. Using the angle subtraction formula for sine, derive the exact value of sin(105°) by expressing 105° as the sum of two standard angles (60° and 45°). Show the derivation step by step, then state the exact simplified value.
3. sin(75°) = ?

…and 4 more problems

1. Liam is designing a triangular support beam for a bridge. One of the angles in the triangle measures 105 degrees. To calculate the exact length of the opposite side using the law of sines, he needs the exact value of sin(105°). Using the angle addition formula for sine, express sin(105°) as a sum of two standard angles (from 30°, 45°, 60°, 90°) whose trigonometric values are known, and derive the exact simplified value of sin(105°).
2. Using the angle addition formula for sine, find the exact value of sin(75°) by expressing it as sin(45° + 30°).
3. cos(195°)cos(45°) + sin(195°)sin(45°) = ?

…and 4 more problems

1. sin(120°)cos(25°) + cos(120°)sin(25°) = ?
2. Aroha is a navigator for a sailing race. The race course requires her to sail at a bearing of 75° from the starting point. To calculate the exact components of her displacement relative to east and north, she needs to know the exact value of sin(75°). Using the angle addition formula sin(A + B) = sin A cos B + cos A sin B, express 75° as the sum of two standard angles (30°, 45°, or 60°) and derive the exact value of sin(75°) in simplest radical form.
3. sin(105°)cos(15°) + cos(105°)sin(15°) = ?

…and 4 more problems