28.Trigonometry Flashcards
What is the definition of trigonometry?
Trigonometry is a branch of mathematics that deals with the relationships between the angles and sides of triangles.
What are the three main trigonometric ratios?
The three main trigonometric ratios are sine (sin), cosine (cos), and tangent (tan).
How do you define sine, cosine, and tangent?
Sine (sin) is the ratio of the length of the opposite side to the length of the hypotenuse. Cosine (cos) is the ratio of the length of the adjacent side to the length of the hypotenuse. Tangent (tan) is the ratio of the length of the opposite side to the length of the adjacent side.
What is the formula for finding the sine of an angle in a right triangle?
sin(A) = opposite / hypotenuse
What is the formula for finding the cosine of an angle in a right triangle?
cos(A) = adjacent / hypotenuse
What is the formula for finding the tangent of an angle in a right triangle?
tan(A) = opposite / adjacent
What is the Pythagorean identity in trigonometry?
The Pythagorean identity states that sin^2(A) + cos^2(A) = 1, where A is an angle in a right triangle.
What are the reciprocal trigonometric ratios?
The reciprocal trigonometric ratios are cosecant (csc), secant (sec), and cotangent (cot), which are the reciprocals of sine, cosine, and tangent, respectively.
What is the formula for finding the cosecant of an angle in a right triangle?
csc(A) = 1 / sin(A)
What is the formula for finding the secant of an angle in a right triangle?
sec(A) = 1 / cos(A)
What is the formula for finding the cotangent of an angle in a right triangle?
cot(A) = 1 / tan(A)
What is the unit circle in trigonometry?
he unit circle is a circle with a radius of 1, centered at the origin of a coordinate plane. It is used to define the values of trigonometric functions for any angle.
What are the periodic properties of trigonometric functions?
Trigonometric functions are periodic, meaning their values repeat after certain intervals. For example, sin(A) and cos(A) have a period of 2π, while tan(A) has a period of π.
What is the relationship between trigonometric functions and right triangles?
Trigonometric functions are defined in terms of ratios of sides in right triangles, but they can also be extended to non-right triangles and angles in the unit circle using the unit circle definitions.
What are the trigonometric identities?
Trigonometric identities are mathematical equations that relate trigonometric functions to each other. Examples include the Pythagorean identities, sum and difference formulas, double angle formulas, and half-angle formulas.
