Skip to main content
Ch. 1 - Functions
Briggs - Calculus: Early Transcendentals 3rd Edition
Briggs3rd EditionCalculus: Early TranscendentalsISBN: 9780136847243Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoBriggs 3rd EditionCh. 1 - FunctionsProblema 7
Capitolo 1, Problema 7

What are the three Pythagorean identities for the trigonometric functions?

Guida verificata passo dopo passo
1
The Pythagorean identities are fundamental relationships between the trigonometric functions sine, cosine, and tangent.
The first Pythagorean identity is derived from the Pythagorean theorem and states: \( \sin^2(\theta) + \cos^2(\theta) = 1 \).
The second identity is obtained by dividing the first identity by \( \cos^2(\theta) \), resulting in: \( 1 + \tan^2(\theta) = \sec^2(\theta) \).
The third identity is derived by dividing the first identity by \( \sin^2(\theta) \), leading to: \( 1 + \cot^2(\theta) = \csc^2(\theta) \).
These identities are useful for simplifying expressions and solving trigonometric equations.

Risposta video verificata per un problema simile:

Questa soluzione video è stata consigliata dai nostri tutor come utile per risolvere questo problema.
Durata del video:
4m

Concetti chiave

Ecco i concetti essenziali che devi comprendere per rispondere correttamente alla domanda.

Pythagorean Identities

Pythagorean identities are fundamental relationships in trigonometry that relate the squares of the sine, cosine, and tangent functions. They stem from the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse equals the sum of the squares of the other two sides. These identities are essential for simplifying trigonometric expressions and solving equations.
Video consigliato:
7:17
Verifying Trig Equations as Identities

Sine and Cosine Relationship

The first Pythagorean identity states that sin²(θ) + cos²(θ) = 1 for any angle θ. This identity illustrates the relationship between the sine and cosine functions, showing that the sum of their squares is always equal to one. It is crucial for understanding the unit circle and the behavior of trigonometric functions.
Video consigliato:
03:53
Derivatives of Sine & Cosine

Tangent and Secant Relationship

The second Pythagorean identity is 1 + tan²(θ) = sec²(θ), which connects the tangent and secant functions. This identity is derived from the first identity by dividing the sine and cosine functions. It is particularly useful in calculus for differentiating and integrating trigonometric functions, as well as in solving trigonometric equations.
Video consigliato:
Percorso guidato
05:13
Slopes of Tangent Lines
Pratica correlata
Domanda del libro di testo

Evaluating functions from graphs Assume ƒ is an odd function and that both ƒ and g are one-to-one. Use the (incomplete) graph of ƒ and g the graph of to find the following function values. <IMAGE>


ƒ(g(4))

553
views
Domanda del libro di testo

Taxicab fees A taxicab ride costs \$3.50 plus \$2.50 per mile. Let m be the distance (in miles) from the airport to a hotel. Find and graph the function c(m) that represents the cost of taking a taxi from the airport to the hotel. Also determine how much it will cost if the hotel is 9 miles from the airport.

312
views
Domanda del libro di testo

Decide whether ff, gg, or both represent one-to-one functions. <IMAGE>

619
views
2
rank
Domanda del libro di testo

How do you obtain the graph of y=f(x+2)y=f\(\left\)(x+2\(\right\)) from the graph of y=f(x)y=f\(\left\)(x\(\right\))?

402
views
Domanda del libro di testo

Solve the equation sin 2Θ = 1, for 0 ≤ Θ < 2π .

321
views
Domanda del libro di testo

Composite functions

Let ƒ(x) = x³, g (x) = sin x and h(x) = √x .

Find the domain of ƒ o g.

489
views