Ch. 2 - Graphs of the Trigonometric Functions; Inverse Trigonometric Functions

Blitzer3rd EditionTrigonometryISBN: 9780137316601Non è quello che usi tu?Cambia libro di testo

Blitzer 3rd Edition

Ch. 2 - Graphs of the Trigonometric Functions; Inverse Trigonometric Functions

Problema 11

Capitolo 2, Problema 11

Solve the right triangle shown in the figure. Round lengths to two decimal places and express angles to the nearest tenth of a degree. b = 2, c = 7

Guida verificata passo dopo passo

Identify the sides and angles in the right triangle. Here, side \(b\) corresponds to \(p = 2\), side \(c\) corresponds to \(r = 7\), and side \(q\) is unknown. Angle \(R\) is the right angle (90°).

Use the Pythagorean theorem to find the length of side \(q\). The formula is \(q = \sqrt{r^2 - p^2}\), where \(r\) is the hypotenuse and \(p\) is one leg of the triangle.

Calculate angle \(Q\) using the sine function: \(\sin(Q) = \frac{p}{r}\). Then find \(Q\) by taking the inverse sine: \(Q = \sin^{-1}\left(\frac{p}{r}\right)\).

Calculate angle \(P\) by subtracting angle \(Q\) from 90°, since the sum of angles in a right triangle is 180° and one angle is 90°. So, \(P = 90^\circ - Q\).

Round the lengths and angles to the required precision: lengths to two decimal places and angles to the nearest tenth of a degree.

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:

Concetti chiave

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

Right Triangle Properties

A right triangle has one angle of 90 degrees. The side opposite this angle is the hypotenuse, the longest side. The other two sides are called legs. Understanding these properties helps identify which sides and angles to use in calculations.

Video consigliato:

Percorso guidato

5:35

30-60-90 Triangles

Pythagorean Theorem

This theorem states that in a right triangle, the square of the hypotenuse equals the sum of the squares of the other two sides (a² + b² = c²). It is essential for finding the length of an unknown side when the other two sides are known.

Video consigliato:

Percorso guidato

5:19

Solving Right Triangles with the Pythagorean Theorem

Trigonometric Ratios (Sine, Cosine, Tangent)

These ratios relate the angles of a right triangle to the lengths of its sides. Sine = opposite/hypotenuse, Cosine = adjacent/hypotenuse, Tangent = opposite/adjacent. They are used to find unknown angles or sides when some measurements are given.

Video consigliato:

Percorso guidato

5:08

Sine, Cosine, & Tangent of 30°, 45°, & 60°

Pratica correlata

Domanda del libro di testo

Determine the amplitude and period of each function. Then graph one period of the function. y = 3 sin (1/2) x

969

views

Domanda del libro di testo

The graph of a cotangent function is given. Select the equation for each graph from the following options: y = cot(x + π/2), y = cot(x + π), y = −cot x, y= −cot(x − π/2).

1996

views

Domanda del libro di testo

Determine the amplitude, period, and phase shift of each function. Then graph one period of the function. y = −3 sin(π/3 x − 3π)

672

views

Domanda del libro di testo

Find the bearing from O to A.

1046

views

Domanda del libro di testo

Graph two periods of the given tangent function. y = tan(x − π/4)