Unit5Vocabulary Flashcards
Inverse Cosine
The inverse of the cosine function that will take a trigonometric ratio as input and produce the angle associated with that ratio. Denoted with a -1 superscript:
cos-1(x)
Angle of Depression
The angular measurement between the horizontal axis down to an object.
Pi
The angular distance between the positive x axis and the negative x axis in radians. Denoted by the Greek letter π it is an irrational number starting with the value 3.1415926…
Inverse Tangent
The inverse of the tangent function that will take a trigonometric ratio as input and produce the angle associated with that ratio. Denoted with a -1 superscript:
tan-1(x)
Sine
Sine of an angle is defined as the ratio of the opposite side over the hypotenuse.
Soh Cah Toa
Side-Side-Angle
This is the case where you have the values of 2 sides and an angle in sequence as you rotate around a triangle in either the clockwise or counter-clockwise direction. This triangle can be solved with the Law of Sines but is known as the Ambiguous case since two possible triangles exist with the same 2 sides and angle.
Cosine
Cosine of an angle is defined as the ratio of the adjacent side over the hypotenuse.
Soh Cah Toa
Law of Cosine
Quotient Identities
Radian
The angular distance of a sector of a circle where the arc length of the sector is equal to the length of the radius.
Tangent
Tangent of an angle is defined as the ratio of the opposite side over the adjacent side.
Soh Cah Toa
Terminal Side
Obtuse Triangle
A triangle that has one angle greater than 90°.
Side-Side-Side
This is when you have the value of all 3 sides of a triangle. This triangle can be solved using the Law of Cosines.
Phase Shift
The horizontal translation of a trigonometric function.
Arc Length
Cosecant
Represented by the letters csc it is an inverse identity as defined below:
Asymptote
A value of the domain for which a function is undefined or for which the range of a function will never exceed. On a graph it is noted as a dotted line which the function’s graph never touches.
Negative Angle Identities
Negative Angles
The angles formed in a unit circle starting with an initial side of the positive x axis and rotating in the clockwise direction around the unit circle.
Circumference
Coterminal Angles
Pythagorean Theorem
The sum of the squares of the legs of a right triangle are equal to the hypotenuse squared.
Inverse Sine
The inverse of the sine function that will take a trigonometric ratio as input and produce the angle associated with that ratio. Denoted with a -1 superscript:
sin-1(x)
Reference Angle
The angle formed between the terminal side of an angle and the x axis when a perpendicular line is dropped to the x axis from the terminal side.
Standard Position
An angle is in standard position if its vertex is located at the origin and one ray is on the positive x-axis.
Cotangent
Represented by the letters cot it is an inverse identity as defined below:
Angle-Angle-Side
In any given triangle, it is when you have the value of 2 angles and 1 side in sequence as you rotate clockwise or counter-clockwise around a triangle. This type of triangle can be solved using the Law of Sines.
Side-Angle-Side
When you have the values of 2 sides and the angle between them in a triangle. This triangle can be solved with the Law of Cosines.
Oblique Triangle
A triangle without any 90° angles.
Radius
The linear distance between the center of a circle and its side.
Law of Sine
Secant
Represented by the letters sec it is an inverse identity as defined below:
Initial Side
The side of an angle that is on the positive x axis in the unit circle.
Area of a Circle
Clinometer
A device that measures angles of elevation or depression.
Period
Defined as the positive x value for which a trigonometric function begins to repeat itself.
Angle-Side-Angle
In any given triangle, it is when you have the value of 2 angles and the side in between them. This type of triangle can be solved using the Law of Cosines.
Degree
Is an angle measurement where the angular distance of a full circle is partitioned into 360 equal parts. One of those parts is considered 1 degree. A degree can be converted to radians using the following:
r/π = d/180
Where r is measurement in radians and d is measurement in degrees.
Acute Triangle
A triangle with all angles measuring less than 90°.
Squared Trignometric Functions
A notation to denote the squaring of the output of a trigonometric function.
Ex: cos2(x) is the same as (cos(x))2
Amplitude
For a sine or cosine graph this is defined as:
A = Maximum - Minimum
2
Cofunction Identities
Angle of Elevation
The angle between the horizontal axis up to an object.
Angle-Angle-Angle
A condition of a triangle where you know all three angles but no sides. This triangle cannot be solved since there are an infinite number of possible solutions.
Pythagorean Identities
Right Triangle
A triangle with one angle equal to 90°.
Unit Circle
A circle with a radius of 1 unit typically inscribed on the cartesian coordinates with the center at the origin.
