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 22
Capitolo 1, Problema 22

Evaluating trigonometric functions Without using a calculator, evaluate the following expressions or state that the quantity is undefined.


tan (15π/4)

Guida verificata passo dopo passo
1
Step 1: Understand the periodicity of the tangent function. The tangent function, \( \tan(\theta) \), has a period of \( \pi \). This means that \( \tan(\theta + n\pi) = \tan(\theta) \) for any integer \( n \).
Step 2: Simplify the angle \( \frac{15\pi}{4} \) by reducing it within the range of \( [0, \pi) \) using the periodicity.
Step 3: Calculate \( \frac{15\pi}{4} \mod \pi \) to find the equivalent angle within one period.
Step 4: Express \( \pi \) in terms of \( \frac{\pi}{4} \) to facilitate the calculation: \( \pi = \frac{4\pi}{4} \).
Step 5: Subtract \( \pi \) from \( \frac{15\pi}{4} \) as many times as needed to bring the angle within the range of \( [0, \pi) \), and then evaluate \( \tan \) at the resulting angle.

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.

Trigonometric Functions

Trigonometric functions, such as sine, cosine, and tangent, relate angles to ratios of sides in right triangles. They are periodic functions, meaning they repeat their values in regular intervals. Understanding these functions is essential for evaluating expressions involving angles, especially when the angles are expressed in radians.
Video consigliato:
Percorso guidato
6:04
Introduction to Trigonometric Functions

Angle Reduction

Angle reduction involves simplifying angles to find equivalent angles within a standard range, typically between 0 and 2π radians. For example, to evaluate tan(15π/4), we can subtract multiples of 2π (or 8π/4) to find a coterminal angle, which makes it easier to compute the tangent value.
Video consigliato:
8:22
Trig Values in Quadrants II, III, & IV Example 2

Undefined Values in Trigonometry

Certain values of trigonometric functions can be undefined, particularly when dealing with tangent and cotangent, which are undefined at odd multiples of π/2. Recognizing these points is crucial when evaluating expressions, as it helps determine whether a function can be computed or if it results in an undefined quantity.
Video consigliato:
Percorso guidato
6:04
Introduction to Trigonometric Functions
Pratica correlata
Domanda del libro di testo

Where do inverses exist? Use analytical and/or graphical methods to determine the largest possible sets of points on which the following functions have an inverse.


{Use of Tech} ƒ(x) = 1/(x-5)

228
views
Domanda del libro di testo

Demand function Sales records indicate that if Blu-ray players are priced at \$250, then a large store sells an average of 12 units per day. If they are priced at \$200, then the store sells an average of 15 units per day. Find and graph the linear demand function for Blu-ray sales. For what prices is the demand function defined?

359
views
Domanda del libro di testo

Evaluating trigonometric functions Without using a calculator, evaluate the following expressions or state that the quantity is undefined.


sec (7π/6)

300
views
Domanda del libro di testo

The population of a small town was 500 in 2018 and is growing at a rate of 24 people per year. Find and graph the linear population function p(t) that gives the population of the town t years after 2018. Then use this model to predict the population in 2033.

587
views
Domanda del libro di testo

Composite functions

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

Find the domain of g o ƒ.

355
views