Domanda del libro di testo
Evaluating trigonometric functions Without using a calculator, evaluate the following expressions or state that the quantity is undefined.
cos (2π/3)
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Ch. 1 - Functions
Briggs3rd EditionCalculus: Early TranscendentalsISBN: 9780136847243
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TOC.tableOfContents
- Ch. 1 - Functions210
- Ch. 2 - Limits371
- Ch. 3 - Derivatives633
- Ch. 4 - Applications of the Derivative412
- Ch. 5 - Integration328
- Ch. 6 - Applications of Integration331
- Ch. 7 - Logarithmic, Exponential Functions, and Hyperbolic Functions177
- Ch. 8 - Integration Techniques394
- Ch. 9 - Differential Equations179
- Ch. 10 - Sequences and Infinite Series339
- Ch. 11 - Power Series218
- Ch.12 - Parametric and Polar Curves215
Briggs3rd EditionCalculus: Early TranscendentalsISBN: 9780136847243Non è quello che usi tu?Cambia libro di testo
Capitolo 1, Problema 19a
Composite functions
Let ƒ(x) = x³, g (x) = sin x and h(x) = √x .
Evaluate h(g( π/2)).
Guida verificata passo dopo passo1
Identify the innermost function in the composite function h(g(\(\pi\)/2)).
Evaluate g(\(\pi\)/2) by substituting \(\pi\)/2 into the function g(x) = \(\sin\) x.
Calculate \(\sin\)(\(\pi\)/2) to find the value of g(\(\pi\)/2).
Substitute the result of g(\(\pi\)/2) into the function h(x) = \(\sqrt{x}\).
Evaluate h(g(\(\pi\)/2)) by calculating \(\sqrt\){g(\(\pi\)/2)).
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Composite Functions
Composite functions are formed when one function is applied to the result of another function. In mathematical notation, if you have two functions f(x) and g(x), the composite function is denoted as (f ∘ g)(x) = f(g(x)). Understanding how to evaluate composite functions is crucial for solving problems that involve multiple functions.
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Evaluate Composite Functions - Special Cases
Function Evaluation
Function evaluation involves substituting a specific input value into a function to obtain an output. For example, if f(x) = x³, then f(2) = 2³ = 8. In the context of composite functions, you first evaluate the inner function and then use that result as the input for the outer function, which is essential for solving the given problem.
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4:26Evaluating Composed Functions
Trigonometric Functions
Trigonometric functions, such as sine (sin), are fundamental in calculus and relate angles to ratios of sides in right triangles. The function g(x) = sin x outputs the sine of the angle x, which is crucial for evaluating composite functions that involve trigonometric expressions. Understanding the properties and values of these functions, especially at key angles, is important for accurate calculations.
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6:04Introduction to Trigonometric Functions
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