Sum Difference Formulas Worksheets Grade 11

1. Mason is analyzing a geometric pattern on a coordinate plane. A right triangle is inscribed in a unit circle with its hypotenuse as the diameter. One acute angle of the triangle measures 75°. Using a sum or difference formula, determine the exact coordinates of the vertex opposite the hypotenuse (the point on the circle that is not an endpoint of the diameter).
2. Mason is a structural engineer analyzing a triangular truss for a bridge design. The truss forms an angle of 105° at one of its joints. Using the sum and difference formulas, determine the exact value of cos(105°).
3. Emma is studying a geometric diagram on a coordinate plane. A point P lies on the unit circle such that the ray from the origin to P makes an angle of 75° with the positive x-axis. Using the sum formula for sine or cosine, determine the exact coordinates of point P.

…and 4 more problems

1. cos(71°)cos(26°) + sin(71°)sin(26°) = ?
2. cos(112°) = cos(70° + 42°) = ?
3. sin(77°)cos(17°) - cos(77°)sin(17°) = ?

…and 4 more problems

1. A right triangle is inscribed in a circle with radius 5 units. The triangle's hypotenuse lies along the diameter of the circle, and one of its acute angles measures 30°. What is the exact length of the side opposite the 30° angle?
2. Matiu is analyzing a geometric pattern formed by two intersecting circles. The circles have equal radii of 14 units and their centers are 14√3 units apart. Consider triangle formed by the two centers and one intersection point of the circles. Using sum or difference formulas for sine or cosine, find the exact value of cos(∠A) where ∠A is the angle at one of the centers in this triangle.
3. sin(127°) = sin(90° + 37°) = ?

…and 3 more problems