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Math
Oklahoma Math
Precalculus (PC): Trigonometry (T)
Draw and recognize angles in standard position using radian measure, and determine the quadrant of the terminal side.
Convert radian measure to degree measure and vice-versa.
Find the length of an arc and the area of a sector on a circle.
- Arc length
- Arc length as fraction of circumference
- Arc length from subtended angle
- Arc length from subtended angle: radians
- Area of a sector
- Area of a sector
- Challenge problems: Arc length (radians) 1
- Challenge problems: Arc length (radians) 2
- Challenge problems: Arc length 1
- Challenge problems: Arc length 2
- Getting ready for circles
- Radians & arc length
Use special triangles to determine geometrically the values of sine, cosine, tangent for , and use the unit circle to express the values of sine, cosine, and tangent for 𝜋 − 𝑥, 𝜋 + 𝑥, and 2𝜋 − 𝑥 in terms of their values for x, where x is any real number.
Use reference angles to determine the terminal point P(x, y) on the unit circle for a given angle.
Estimate trigonometric values of any angle.
Apply the properties of a unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions.
Graph of all six trigonometric functions, identifying key features.
- Amplitude of sinusoidal functions from graph
- Features of sinusoidal functions
- Graph of y=sin(x)
- Graph of y=tan(x)
- Intersection points of y=sin(x) and y=cos(x)
- Midline of sinusoidal functions from equation
- Midline of sinusoidal functions from graph
- Midline, amplitude, and period review
- Period of sinusoidal functions from graph
Describe and analyze the relationships of the properties of a unit circle.
Create models for situations involving trigonometry.
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Apply the Law of Sines and Law of Cosines to solve problems.
- General triangle word problems
- Laws of sines and cosines review
- Solve triangles using the law of cosines
- Solve triangles using the law of sines
- Solving for a side with the law of cosines
- Solving for a side with the law of sines
- Solving for an angle with the law of cosines
- Solving for an angle with the law of sines
- Trig word problem: stars
Use trigonometry to find the area of triangles.
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Use inverse functions to solve trigonometric equations; evaluate the solution and interpret them in terms of context.
- Cosine equation algebraic solution set
- Cosine equation solution set in an interval
- Evaluate inverse trig functions
- Intro to arccosine
- Intro to arcsine
- Intro to arctangent
- Inverse trigonometric functions review
- Solve sinusoidal equations
- Solve sinusoidal equations (basic)
- Solving sinusoidal equations of the form sin(x)=d
- Trigonometric equations review
- Using inverse trig functions with a calculator
Algebraically manipulate the structure of a trigonometric expression to identify ways to rewrite it.
- Proof of the Pythagorean trig identity
- Pythagorean identity review
- Sine & cosine identities: periodicity
- Sine & cosine identities: symmetry
- Tangent identities: symmetry
- Use the Pythagorean identity
- Using the Pythagorean trig identity
- Using trig angle addition identities: manipulating expressions
- Using trigonometric identities
Choose and produce an equivalent form of an expression to explain the properties of the quantity represented by the expression.
Graphically and algebraically verify solutions to trigonometric equations.
Use the relation 𝑖^2 = −1 and the mathematical properties to add, subtract, and multiply complex numbers.
- Add & subtract complex numbers
- Adding complex numbers
- Classifying complex numbers
- Complex number conjugates
- Complex number operations review
- Complex number polar form review
- Complex numbers: FAQ
- Graphically add & subtract complex numbers
- Graphically multiply complex numbers
- Intro to complex number conjugates
- Intro to the imaginary numbers
- Multiply & divide complex numbers in polar form
- Multiply complex numbers
- Multiplying complex numbers
- Multiplying complex numbers graphically example: -1-i
- Multiplying complex numbers graphically example: -3i
- Multiplying complex numbers in polar form
- Subtracting complex numbers
- Visualizing complex number multiplication
- Visualizing complex number powers
Find the conjugate of a complex number in rectangular forms and quotients of complex numbers.
- Complex number conjugates
- Complex number conjugates
- Complex number polar form review
- Complex numbers: FAQ
- Divide complex numbers
- Dividing complex numbers
- Dividing complex numbers review
- Intro to complex number conjugates
- Multiply & divide complex numbers in polar form
- Visualizing complex number multiplication
Solve quadratic equations in one variable that have complex solutions.