alleryStart learning →The Pythagorean identities of trigonometry are built on the properties of which figure?
AThe right triangle
BThe regular hexagon
CThe isosceles trapezium
DThe equilateral rhombus
Answer & Solution
Correct answer: A. The right triangle
1. The three Pythagorean identities are sin^2 x + cos^2 x = 1, 1 + cot^2 x = csc^2 x and 1 + tan^2 x = sec^2 x.
2. All three are equations involving trigonometric functions that rest on the properties of a right triangle.
3. The hexagon, the trapezium and the rhombus carry no such ratio of opposite, adjacent and hypotenuse, so none of them generates these identities.
_Source: OpenStax Algebra and Trigonometry (CC BY 4.0), Ch 9 "Trigonometric Identities and Equations", section 9.1 Solving Trigonometric Equations with Identities_
Keep practising Trigonometric Identities and Equations
Browse all Trigonometric Identities and Equations questions for B.Sc Mathematics, or explore more Mathematics topics.
Related questions
If a ladder's base is a feet from the wall and its length is 4a feet, how high up the wallSafety rules place a ladder's base 1 foot from the wall for every 4 feet of ladder length.Compared with y = sin t, the graph of y = sin(2t) is which transformation?Solving sin(n t) = c across one turn requires going around the unit circle how many times?Solve cos(2t) = 1/2 on the interval from 0 to 2 pi.Solve 3 cos t + 3 = 2 sin^2 t exactly on the interval from 0 to 2 pi.Solve cos t cos(2t) + sin t sin(2t) = sqrt(3)/2 on the interval from 0 to 2 pi.Solve 2 sin^2 t + sin t = 0 exactly on the interval from 0 to 2 pi.