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AP Calculus AB: 5.1.1 A Review of Trigonometry

Mathematics13 CardsCreated 3 months ago

This flashcard set provides a comprehensive review of fundamental trigonometric concepts, including the Pythagorean identity and basic trig functions. It also includes practice problems focused on simplifying trigonometric expressions using identities and reciprocal relationships between functions.

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A Review of Trigonometry

  • The Pythagorean theorem relates the sides of a right triangle. Each trigonometric function matches the ratio of two sides of a right triangle to one of the angles.

  • The Pythagorean identity is sin^2x+cos^2x=1

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Key Terms

Term
Definition

A Review of Trigonometry

  • The Pythagorean theorem relates the sides of a right triangle. Each trigonometric function matches the ratio of two sides of a right triang...

note

  • Trigonometry examines the relationships between the lengths of the sides of a right triangle and one of the acute angles of that triangle.<...

Simplify the expression: sin(x)/cos(x) ⋅ cot(x)

1

Simplify the expression: sin(x) ⋅ sec(x) ⋅ tan(x) − sec^2(x)

-1

Simplify the expression: sec(x) ⋅ csc(x) ⋅ cot(x)

csc^2 (x)

Simplify the expression: cscx/sinx−cot^2x

1

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AP Calculus AB: 5.1.1 A Review of Trigonometry
TermDefinition

A Review of Trigonometry

  • The Pythagorean theorem relates the sides of a right triangle. Each trigonometric function matches the ratio of two sides of a right triangle to one of the angles.

  • The Pythagorean identity is sin^2x+cos^2x=1

note

  • Trigonometry examines the relationships between the lengths of the sides of a right triangle and one of the acute angles of that triangle.

  • The most important identity to remember in trigonometry is the Pythagorean theorem. This theorem is the foundation of trigonometry.

  • The three most basic trig functions are the sine function, the cosine function, and the tangent function. Each is defined for a given angle by the ratio of two of the sides of a right triangle.

  • Notice that the tangent function can be expressed in terms of the sine and cosine functions.

  • The reciprocal trig functions are defined by reciprocal
    relationships with the three basic trig functions. The
    reciprocal functions are the cosecant function, the
    secant function, and the cotangent function.

  • Notice that the reciprocal of sin θ is csc θ, not sec θ.

  • There are some notation conventions that you should be aware of regarding trig functions. Notice that if a trig function is raised to a power, then the exponent can either appear after the name of the trig function or outside of the function surrounded, by parentheses. If you do not include the parentheses, it is easy to confuse the meaning of the exponent.

  • There are many relationships between the different
    trigonometric functions. The most fundamental is the
    Pythagorean identity.

  • The Pythagorean identity states that the square of the sine of any angle plus the square of the cosine of that angle is equal to 1.

  • You can prove the Pythagorean identity using the Pythagorean theorem.

Simplify the expression: sin(x)/cos(x) ⋅ cot(x)

1

Simplify the expression: sin(x) ⋅ sec(x) ⋅ tan(x) − sec^2(x)

-1

Simplify the expression: sec(x) ⋅ csc(x) ⋅ cot(x)

csc^2 (x)

Simplify the expression: cscx/sinx−cot^2x

1

Simplify the expression:sinx⋅1/cosx

tan x

Simplify the expression:cosx⋅1/sinx

cot x

Simplify the expression:sin(x)⋅1/csc(x)+cos(x)⋅1/sec(x)

1

Simplify the expression:tanx⋅cosx

sin x

Simplify the expression:sin(x)⋅1/sec(x)−cos(x)⋅1/csc(x)

0

Evaluate the following expression exactly using trigonometric identities.sin^2 π/10+cos^2 π/10

1

Simplify the expression:tanx⋅cos^2x

sin x cos x