Sum Difference Formulas Worksheets Grade 11

1. cos(285°) = ?
2. cos(165°) = ?
3. Aroha is a marine biologist studying the depth of a tidal channel. She models the depth of the water, in meters, at time t hours after midnight using the function D(t) = 12sin(πt/6) + 5cos(πt/6). To predict the maximum depth for a safe navigation report, Aroha needs to rewrite this expression in the form Rsin(πt/6 + α). Determine the exact value of the amplitude R.

…and 5 more problems

1. Olivia is studying the path of a projectile in her physics class. The height of the projectile at time t seconds is given by h(t) = 3 sin(5t) + 4 cos(5t). Using the sum formula for sine, rewrite h(t) in the form R sin(5t + α) and determine the exact amplitude R of the projectile's motion.
2. Liam is designing a suspension bridge and needs to calculate the exact height of the main cable at a point 30 meters from the center of the bridge. The cable follows a parabolic curve described by the equation y = 25 - (x²/36), where y is the height in meters and x is the horizontal distance from the center. Using trigonometric identities, determine the exact height of the cable when x = 30 meters.
3. cos(105°) = cos(45° + 60°) = ?

…and 4 more problems

1. A triangle is inscribed in a circle with radius 8 cm. Two sides of the triangle measure 12 cm and 10 cm, and the angle between them is 60°. Using the Law of Cosines, find the length of the third side of the triangle.
2. sin(105°) = sin(75° + 30°) = ?
3. Emma is analyzing sound waves in her physics class and needs to find the exact value of sin(75°) for a wave interference calculation. Using sum and difference formulas, determine the exact value of sin(75°).

…and 4 more problems