Algebra 2 w/ Trig Unit 5 Vocabulary

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.

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.