Algebra 2 w/ Trig Unit 5 Vocabulary
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Questions and Answers

What is sine?

The trigonometric function that is equal to the ratio of the side opposite a given angle to the hypotenuse.

What is cosine?

The trigonometric function that is equal to the ratio of the side adjacent a given angle to the hypotenuse.

What is tangent?

The length of the opposite side divided by the length of the adjacent side.

What is cosecant?

<p>The ratio of the hypotenuse to the side opposite an acute angle; the reciprocal of sine.</p> Signup and view all the answers

What is secant?

<p>The ratio of the hypotenuse to the shorter side adjacent to an acute angle; the reciprocal of cosine.</p> Signup and view all the answers

What is cotangent?

<p>The ratio of the side adjacent to a particular acute angle to the side opposite the angle.</p> Signup and view all the answers

What is the angle of elevation?

<p>The angle formed by the line of sight and the horizontal plane for an object above the horizontal.</p> Signup and view all the answers

What is the angle of depression?

<p>The angle formed by the line of sight and the horizontal plane for an object below the horizontal.</p> Signup and view all the answers

What is standard position in trigonometry?

<p>An angle lying in the Cartesian plane whose vertex is at the origin and whose initial ray lies along the positive x-axis.</p> Signup and view all the answers

What is terminal side?

<p>A straight line that has been rotated around a point on another line to form an angle measured in a clockwise or counterclockwise direction.</p> Signup and view all the answers

What is initial side?

<p>A stationary straight line that contains a point about which another straight line is rotated to form an angle.</p> Signup and view all the answers

What is the unit circle?

<p>A circle with a radius of one centered at the origin in the Cartesian coordinate system.</p> Signup and view all the answers

What is a radian?

<p>A unit of angle, equal to an angle at the center of a circle whose arc is equal in length to the radius.</p> Signup and view all the answers

What is a coterminal angle?

<p>Angles in standard position that have a common terminal side.</p> Signup and view all the answers

What is a quadrantal angle?

<p>An angle with its terminal side on the x-axis or y-axis.</p> Signup and view all the answers

What is a reference angle?

<p>The positive acute angle formed by the x-axis and the terminal side of a given angle.</p> Signup and view all the answers

What is the Law of Sines?

<p>The relationship between the sides and angles of non-right triangles; it states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is the same for all sides and angles in a given triangle.</p> Signup and view all the answers

What is the Law of Cosines?

<p>The square of a side of a plane triangle equals the sum of the squares of the remaining sides minus twice the product of those sides and the cosine of the angle between them.</p> Signup and view all the answers

What does periodic mean in mathematics?

<p>A function that repeats its values in regular intervals or periods.</p> Signup and view all the answers

What is amplitude?

<p>The height from the midline to the max or min.</p> Signup and view all the answers

What is phase shift?

<p>A horizontal shift for a periodic function.</p> Signup and view all the answers

What is period in trigonometry?

<p>The distance required for the function to complete one full cycle.</p> Signup and view all the answers

What is midline?

<p>A horizontal axis that is used as the reference line about which the graph of a trigonometric function oscillates.</p> Signup and view all the answers

Study Notes

Trigonometric Functions

  • Sine: Ratio of the length of the side opposite a given angle to the hypotenuse.
  • Cosine: Ratio of the length of the side adjacent to a given angle to the hypotenuse.
  • Tangent: Ratio of the opposite side to the adjacent side.
  • Cosecant: Reciprocal of sine; ratio of the hypotenuse to the opposite side.
  • Secant: Reciprocal of cosine; ratio of the hypotenuse to the adjacent side.
  • Cotangent: Ratio of the adjacent side to the opposite side of an acute angle.

Geometry of Angles

  • Angle of Elevation: Angle between the line of sight and the horizontal when viewing an object above.
  • Angle of Depression: Angle between the line of sight and the horizontal when viewing an object below.
  • Standard Position: Angle whose vertex is at the origin, starting along the positive x-axis.
  • Terminal Side: The straight line formed by rotating an initial ray to create an angle in either direction.
  • Initial Side: The stationary ray from which an angle is measured.

Circle and Angle Measurements

  • Unit Circle: Circle with a radius of one, centered at the origin in the Cartesian plane, crucial for trigonometric functions.
  • Radian: Unit of angle measurement where the length of the arc equals the circle's radius.
  • Coterminal Angle: Angles in standard position sharing the same terminal side.
  • Quadrantal Angle: Angle with terminal side aligned with the x-axis or y-axis.
  • Reference Angle: Acute angle formed between the terminal side of an angle in standard position and the x-axis.

Laws of Trigonometry

  • Law of Sines: Describes the relationship between sides and angles in non-right triangles, stating that the ratio of a side's length to the sine of its opposite angle is constant for all sides and angles.
  • Law of Cosines: Relates the lengths of the sides of a triangle to the cosine of one of its angles.

Characteristics of Periodic Functions

  • Periodic: Function that repeats values at regular intervals.
  • Amplitude: Measurement from the midline to the maximum or minimum value of a periodic function.
  • Phase Shift: Horizontal displacement of a periodic function.
  • Period: Distance required for a periodic function to complete one full cycle.
  • Midline: A horizontal axis that serves as the reference line around which a trigonometric function oscillates.

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Description

This quiz consists of vocabulary flashcards for Unit 5 of Algebra 2 with Trigonometry. Each card provides definitions for essential trigonometric functions such as sine, cosine, and tangent. Test your knowledge and familiarize yourself with these key terms to enhance your understanding of trigonometry.

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