6.3: Inverse Trigonometric Functions
Domain and Range of Trigonometric Functions The domain of a function is the specific set of values that the independent variable in a function can take on. The range is the resulting values that the dependant variable can have as x varies throughout the domain. Domain and range for sine and cosine functions. Hence, for the trigonometric functions f (x)= sin x and f (x)= cos x, the domain will consist of the entire set of real numbers, as they are defined for all the real numbers. The range of f (x) = sin x and f (x)= cos x will lie from -1 to 1, including both -1 and +1, i.e. -1 ? sin x ?1 -1 ? cos x ?1.
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Finding the Exact Value of Expressions Involving the Inverse Sine, Cosine, and Tangent Functions
Range of a trig function The range of a function consists of all its output values — the numbers you get when you input numbers from the domain into the function and perform the function operations on them. Sometimes, a range can be all possible real numbers — it has no limit. That situation happens in a function such as h (x) = 3 x + 2. Nov 20, · For the function y = f (x), all the values that x can take become the domain of the function and all of the output values that y takes become the range of the function. Trigonometric functions are. A function consists of a rule that you apply to the input values. The result is a single output value. You can usually use a huge number of input values, and they’re all part of the domain of the function. The output values make up the range of the function. Domain of a trig function [ ].
Algebra all content. Introduction to radians. Intro to radians Opens a modal. Degrees to radians Opens a modal. Radians to degrees Opens a modal. Unit circle Opens a modal. Trig unit circle review Opens a modal. Basic trigonometric identities. Tangent identities: symmetry Opens a modal. Tangent identities: periodicity Opens a modal.
Trigonometric values of special angles. Trig values of special angles. Pythagorean identity. Proof of the Pythagorean trig identity Opens a modal. Using the Pythagorean trig identity Opens a modal. Pythagorean identity review Opens a modal. Use the Pythagorean identity. Features of sinusoidal functions Opens a modal. Midline of sinusoidal functions from graph.
Amplitude of sinusoidal functions from graph. Midline of sinusoidal functions from equation. Amplitude of sinusoidal functions from equation. Period of sinusoidal functions. Midline, amplitude, and period review Opens a modal. Period of sinusoidal functions from graph. Period of sinusoidal functions from equation. Graphing sinusoidal functions. Graph sinusoidal functions. Constructing sinusoidal functions. Sinusoidal function from graph Opens a modal.
Trig word problem: modeling daily temperature Opens a modal. Trig word problem: modeling annual temperature Opens a modal. Construct sinusoidal functions. Modeling with sinusoidal functions. The inverse trigonometric functions. Intro to arcsine Opens a modal. Intro to arctangent Opens a modal. Intro to arccosine Opens a modal.
Restricting domains of functions to make them invertible Opens a modal. Using inverse trig functions with a calculator Opens a modal. Inverse trigonometric functions review Opens a modal. Evaluate inverse trig functions.
Solving basic sinusoidal equations. Solve sinusoidal equations basic. Solving advanced sinusoidal equations. Solve sinusoidal equations. Solving sinusoidal models. Trig word problem: solving for temperature Opens a modal. Trigonometric equations review Opens a modal. Sinusoidal models word problems.
Introduction to the trigonometric angle addition identities. Review of trig angle addition identities Opens a modal. Using the cosine angle addition identity Opens a modal. Using the cosine double-angle identity Opens a modal. Proof of the sine angle addition identity Opens a modal.
Proof of the cosine angle addition identity Opens a modal. Using the trig angle addition identities. Using trigonometric identities to solve problems. Finding trig values using angle addition identities Opens a modal. Using trig angle addition identities: finding side lengths Opens a modal. Using trig angle addition identities: manipulating expressions Opens a modal. Using trigonometric identities Opens a modal. Find trig values using angle addition identities.
Parametric equations. Parametric equations intro Opens a modal. Removing the parameter in parametric equations Opens a modal. Removing the parameter in parametric equations example 2 Opens a modal. Parametric equations with the same graph Opens a modal. Unit test.
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