Basic_trigonometric_identities
Learn about very useful trigonometric identities that arise by considering different properties of the unit circle definition.
Learn about radians, which are the official unit of measurement for angles in algebra (in contrast to degrees, which are used in geometry).
The_inverse_trigonometric_functions
Learn about the inverse functions of sine, cosine, and tangent, and how they are defined even though the functions are not really invertible. These functions will be very helpful when you will solve trigonometric equations.
Feel that Cartesian coordinates are too "square". That they bias us towards lines and away from cool spirally things. Well polar coordinates be just what you need!
Learn how to draw the graph of sinusoidal functions. For example, draw the graph of f(x)=-2*cos(πx)-7.
Prove the Pythagorean trigonometric identity for all real numbers and use it in order to solve problems.
Trigonometric_values_of_special_angles
Learn how to find the trigonometric values of some special angles without the use of a calculator.
Finding_amplitude_midline_of_sinusoidal_functions_from_their_formulas
Learn how to find the amplitude and the midline of the graph of a sinusoidal function from its formula. For example, find the amplitude and the midline of f(x)=3*sin(2x-1)+5.
Solve word problems that involve sinusoidal modeling functions.
Constructing_sinusoidal_functions
Learn how to find the formula of a sinusoidal function from its graph or a few selected features. Model real-world situations with sinusoidal functions.
Solving_basic_sinusoidal_equations
Learn how to solve equations of the form sin(x)=d or cos(x)=d where d is any number. For example, solve sin(x)=0.6.
Here we will explore representing our x's and y's in terms of a third variable or parameter (often 't'). Not only can we describe new things, but it can be super useful for describing things like particle motion in physics.
Period_of_sinusoidal_functions
Learn about the period of sinusoidal functions: how it relates to extremum points and the midline, and how to find it from the formula of the function. For example, find the period of f(x)=3*sin(2x-1)+5.
The_unit_circle_definition_of_sine_cosine_tangent
Learn how the trigonometric ratios are extended to all real numbers using algebra. Start solving simple problems that involve this new definition of the trigonometric functions.
Introduction_to_amplitude_midline_extrema_of_sinusoidal_functions
Learn about very important features of sinusoidal functions: the amplitude and the midline. Learn how they relate to the extremum points of the function.
The_graphs_of_sine_cosine_tangent
Learn how the graphs of y=sin(θ), y=cos(θ), and y=tan(θ) look, using the unit circle definition of the functions.
Solving_advanced_sinusoidal_equations
Learn how to solve equations of the form a*sin(bx+c)=d or a*cos(bx+c)=d where a, b, c, and d are any number. For example, solve 5*sin(2x-1)=3.
Using_trigonometric_identities_to_solve_problems
Learn about different ways in which trigonometric identities, such as the Pythagorean identity and the angle addition identities, can be used to solve problems.
Introduction_to_the_trigonometric_angle_addition_identities
Learn about the trigonometric angle addition identities, which help us discuss the trig values of sums of angles in terms of the trig values of the individual angles. For example, we can express sin(x+y) in terms of sin(x), sin(y), cos(x), and cos(y).
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