B.Sc Mathematics — free MCQ practice

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_

1. The even-odd identities are statements such as sin(-x) = -sin x and cos(-x) = cos x. 2. Each one links the value of a function at an angle to its value at the opposite angle, that is, at the negative of that angle. 3. Doubling the angle is the business of the double-angle formulas, and complements belong to the cofunction identities. _Source: OpenStax Algebra and Trigonometry (CC BY 4.0), Ch 9 "Trigonometric Identities and Equations", section 9.1 Solving Trigonometric Equations with Identities_

1. An even function satisfies f(-x) = f(x), and cos(-x) = cos x, so cosine is even. 2. Secant is the reciprocal of cosine, so sec(-x) = 1 / cos(-x) = 1 / cos x = sec x, making secant even too. 3. Sine, cosecant, tangent and cotangent all reverse sign under a negative angle, so those four are odd. 4. Exactly two functions are even, and they are cosine and secant. _Source: OpenStax Algebra and Trigonometry (CC BY 4.0), Ch 9 "Trigonometric Identities and Equations", section 9.1 Solving Trigonometric Equations with Identities_