Podcast
Questions and Answers
The set of Natural Numbers includes the number zero.
The set of Natural Numbers includes the number zero.
False (B)
The interval (3, 5) contains the endpoints 3 and 5.
The interval (3, 5) contains the endpoints 3 and 5.
False (B)
The intersection of two sets A and B, A ∩ B, contains all elements found in either A or B.
The intersection of two sets A and B, A ∩ B, contains all elements found in either A or B.
False (B)
Multiplying both sides of the inequality n < 5 by -1 reverses the direction of the inequality sign.
Multiplying both sides of the inequality n < 5 by -1 reverses the direction of the inequality sign.
Irrational Numbers can be expressed as a fraction of two integers.
Irrational Numbers can be expressed as a fraction of two integers.
The symbol Ø represents a set with at least one element.
The symbol Ø represents a set with at least one element.
If A = {1, 2, 3} and B = {3, 4, 5}, then A ∩ B = {3}.
If A = {1, 2, 3} and B = {3, 4, 5}, then A ∩ B = {3}.
The cardinality of set C = {1, 2, 3} is 4.
The cardinality of set C = {1, 2, 3} is 4.
In set builder notation, the expression {x | x is an odd number} would define the set of all odd numbers.
In set builder notation, the expression {x | x is an odd number} would define the set of all odd numbers.
The difference of sets A and B, denoted A ackslash B, contains elements that are in set B but not in set A.
The difference of sets A and B, denoted A ackslash B, contains elements that are in set B but not in set A.
A positive angle is measured clockwise from the positive x-axis.
A positive angle is measured clockwise from the positive x-axis.
The sine of 60° is equal to √3/2.
The sine of 60° is equal to √3/2.
Secant of π/3 is equal to 1/2.
Secant of π/3 is equal to 1/2.
The cosine function is classified as an odd function.
The cosine function is classified as an odd function.
The value of tan(π/4) is 1.
The value of tan(π/4) is 1.
A positive angle is measured clockwise.
A positive angle is measured clockwise.
An angle is in standard position when its vertex is at the origin of an xy-plane.
An angle is in standard position when its vertex is at the origin of an xy-plane.
One degree can be divided into 3600 seconds.
One degree can be divided into 3600 seconds.
The formula for converting degrees to radians is θ = length of radius / 2.
The formula for converting degrees to radians is θ = length of radius / 2.
The circumference of a circle can be calculated using the formula C = 2πr.
The circumference of a circle can be calculated using the formula C = 2πr.
The sum of all angles in a triangle is 180°.
The sum of all angles in a triangle is 180°.
An obtuse angle measures exactly 90°.
An obtuse angle measures exactly 90°.
The Pythagorean Theorem states that $a^2 + b^2 = c^2$ where 'c' is the longest side of a right triangle.
The Pythagorean Theorem states that $a^2 + b^2 = c^2$ where 'c' is the longest side of a right triangle.
If two triangles are similar, they must have different angles.
If two triangles are similar, they must have different angles.
SOH CAH TOA is used to remember the definitions of sine, cosine, and tangent for right triangles.
SOH CAH TOA is used to remember the definitions of sine, cosine, and tangent for right triangles.
$sin^{2}θ + cos^{2}θ = 2$ is a correct mathematical identity.
$sin^{2}θ + cos^{2}θ = 2$ is a correct mathematical identity.
For a right triangle, it is true that $tanθ = cot(90-θ)$.
For a right triangle, it is true that $tanθ = cot(90-θ)$.
$secθ$ is equal to the reciprocal of $cosθ$.
$secθ$ is equal to the reciprocal of $cosθ$.
The equation $tan^{2}θ + 1 = sec^{2}θ$ can be calculated as $3^{2} + 1 = sec^{2}θ$.
The equation $tan^{2}θ + 1 = sec^{2}θ$ can be calculated as $3^{2} + 1 = sec^{2}θ$.
$cot(90-θ) = secθ$ is a valid equation.
$cot(90-θ) = secθ$ is a valid equation.
A function can have multiple outputs for a single input.
A function can have multiple outputs for a single input.
The range of a function consists of all possible inputs.
The range of a function consists of all possible inputs.
The cosine function is bounded between -1 and 1.
The cosine function is bounded between -1 and 1.
Function composition can be visualized as chaining one function after another.
Function composition can be visualized as chaining one function after another.
In the function f(x) = x^2, f(-2) results in the same output as f(2).
In the function f(x) = x^2, f(-2) results in the same output as f(2).
In a 45/45/90 triangle, the sine of the angle is equal to the cosine of the angle.
In a 45/45/90 triangle, the sine of the angle is equal to the cosine of the angle.
In a 30/60/90 triangle, if the length of the shortest side is 1, the length of the hypotenuse is $ rac{1}{2}$.
In a 30/60/90 triangle, if the length of the shortest side is 1, the length of the hypotenuse is $ rac{1}{2}$.
The perimeter of a square with a diagonal of 10 meters is $20 ext{√}2$ meters.
The perimeter of a square with a diagonal of 10 meters is $20 ext{√}2$ meters.
The height of an equilateral triangle with side length 12 cm is $6 ext{√}2$ cm.
The height of an equilateral triangle with side length 12 cm is $6 ext{√}2$ cm.
In a 30/60/90 triangle, the ratio of the lengths of the sides opposite the 30°, 60°, and 90° angles is 1 : $ ext{√}3$ : 2.
In a 30/60/90 triangle, the ratio of the lengths of the sides opposite the 30°, 60°, and 90° angles is 1 : $ ext{√}3$ : 2.
For the functions f(x) = x² + 8 and g(x) = x - 3, (g o f)(2) equals 17.
For the functions f(x) = x² + 8 and g(x) = x - 3, (g o f)(2) equals 17.
The function f(x) = 4x + 1 and g(x) = 4x - 1 are inverses of each other.
The function f(x) = 4x + 1 and g(x) = 4x - 1 are inverses of each other.
The notation f: D → R indicates that f takes inputs from domain D and produces outputs in range R.
The notation f: D → R indicates that f takes inputs from domain D and produces outputs in range R.
The composition of functions g and f is defined as (g o f)(x) = f(g(x)).
The composition of functions g and f is defined as (g o f)(x) = f(g(x)).
The expression (g o f)(x) for functions g(x) = x + 1 and f(x) = √(5x - 15) + 1 reduces to √(5x - 15) + 2.
The expression (g o f)(x) for functions g(x) = x + 1 and f(x) = √(5x - 15) + 1 reduces to √(5x - 15) + 2.
200.805° is equivalent to 200° 48' 18".
200.805° is equivalent to 200° 48' 18".
3 radians is equal to 180°.
3 radians is equal to 180°.
If two angles are co-terminal, then their difference is 180°.
If two angles are co-terminal, then their difference is 180°.
1 radian equals $ rac{180°}{ ext{π}}$.
1 radian equals $ rac{180°}{ ext{π}}$.
The angle 150° is equal to $ rac{5 ext{π}}{6}$ radians.
The angle 150° is equal to $ rac{5 ext{π}}{6}$ radians.
Flashcards
Set
Set
A collection of distinct objects. Each object is called an element.
Cardinality
Cardinality
The number of elements in a set.
Empty Set
Empty Set
A set with no elements.
Union of Sets (A ∪ B)
Union of Sets (A ∪ B)
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Intersection of Sets (A ∩ B)
Intersection of Sets (A ∩ B)
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Degrees
Degrees
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Radians
Radians
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Congruent angles
Congruent angles
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Co-terminal angles
Co-terminal angles
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Degrees to Radians Conversion
Degrees to Radians Conversion
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Triangle Angle Sum Theorem
Triangle Angle Sum Theorem
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Rational Numbers (ℚ)
Rational Numbers (ℚ)
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Real Numbers (ℝ)
Real Numbers (ℝ)
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Isosceles Triangle
Isosceles Triangle
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Irrational Numbers (ℝ \ ℚ)
Irrational Numbers (ℝ \ ℚ)
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Equilateral Triangle
Equilateral Triangle
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Right Triangle
Right Triangle
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Interval (a, ∞)
Interval (a, ∞)
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Closed Interval [a, b]
Closed Interval [a, b]
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Pythagorean Theorem
Pythagorean Theorem
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What is an angle?
What is an angle?
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Standard Position
Standard Position
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Positive and Negative Angles
Positive and Negative Angles
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Positive Angle
Positive Angle
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Sine and Cosine of Complementary Angles
Sine and Cosine of Complementary Angles
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Tangent and Cotangent of Complementary Angles
Tangent and Cotangent of Complementary Angles
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Negative Angle
Negative Angle
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Pythagorean Identity
Pythagorean Identity
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Sine (sin θ)
Sine (sin θ)
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Tangent-Secant Identity
Tangent-Secant Identity
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Cosine (cos θ)
Cosine (cos θ)
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Cotangent-Cosecant Identity
Cotangent-Cosecant Identity
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Cosine of a Negative Angle (cos(-θ))
Cosine of a Negative Angle (cos(-θ))
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Sine and Cosine in 45-45-90 Triangle
Sine and Cosine in 45-45-90 Triangle
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Tangent in 45-45-90 Triangle
Tangent in 45-45-90 Triangle
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30-60-90 Triangle: Short Side
30-60-90 Triangle: Short Side
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30-60-90 Triangle: Longer Leg
30-60-90 Triangle: Longer Leg
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Perimeter of a Square with Diagonal
Perimeter of a Square with Diagonal
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What is a function?
What is a function?
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What is the domain of a function?
What is the domain of a function?
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What is the range of a function?
What is the range of a function?
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What is function composition?
What is function composition?
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What is an even function?
What is an even function?
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Function Composition
Function Composition
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g o f (g composed with f)
g o f (g composed with f)
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Inverse Functions
Inverse Functions
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Inverse Function Property
Inverse Function Property
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Checking for Inverse Functions
Checking for Inverse Functions
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