Pythagorean Identity Applications Worksheets Grade 11

1. If cos θ = -8/17 and θ is in quadrant II, find sin θ = ?
2. If sin θ = -5/13 and θ is in quadrant IV, find cos θ = ?
3. If sin θ = -11/61 and θ is in quadrant IV, find cos θ = ?

…and 4 more problems

1. Liam is designing a triangular support structure for a bridge. The structure forms a right triangle where the hypotenuse measures 13 meters and one of the acute angles is θ. Given that sin(θ) = 5/13, determine the exact value of cos(θ) and tan(θ) using the Pythagorean identity.
2. Liam is designing a suspension bridge where the main cable forms a parabolic shape. At a point 50 meters horizontally from the lowest point of the cable, the cable makes an angle of 30° with the horizontal. If the cable's slope at any point is given by tan(θ), use the Pythagorean identity to find the exact value of sin(θ) at this location.
3. Mason is an engineer designing a magnetic levitation train. The vertical force component acting on a test carriage is proportional to sin(θ), where θ is the angle of the guideway relative to the horizontal. At a specific test point, the control system measures cos(θ) = -7/11, and the angle θ is in Quadrant II. To calculate the required current for the lifting electromagnets, Mason needs the exact value of sin(θ) using the Pythagorean identity. What is the exact value of sin(θ)?

…and 4 more problems

1. If sin θ = -15/17 and θ is in quadrant III, find cos θ = ?
2. Sophia is designing a sound wave model for a physics experiment. The displacement of a particle in the medium is given by y = A sin(θ), where A is the amplitude. At a particular instant, she determines that cos(θ) = 1/6. To calculate the particle's velocity, she needs the exact value of sin(θ) using the Pythagorean identity, given that θ is in Quadrant II. What is the exact value of sin(θ)?
3. If sin θ = -4/5 and θ is in quadrant III, find cos θ = ?

…and 5 more problems