Find all solutions The image contains handwritten equations and solutions that appear to be from a mathematics exercise focusing on trigonometric identities and equations. ---Equation 21: The problem is:\[ 4\sin\theta - 1 = 2\sin\theta \]To solve for $\sin\theta$:\[ \sin\theta = \frac{2\sin\theta + 1}{4} \]---Next to the equations for Exercise 21, there are unrelated mathematical solutions without clear instructions:\[ \frac{2\pi}{3} + 2\pi n \]\[ \frac{\pi}{3} + \pi n \]Equation 29:Given:\[ \tan 3x = \]Solutions are partially visible:\[ 3x = \frac{\pi}{6} \]These sections are part of solving trigonometric equations to find the angles that satisfy the equation, given $\theta$ or $x$ in trigonometric functions. The letters $n$ typically denote any integer, suggesting multiple solutions based on periodic properties of trigonometric functions.

Name: Find all solutions The image contains handwritten equations and soluti
Uploaded: 2024-03-20T07:07:26.000Z
Channel: Bartleby
Description: Find all solutions The image contains handwritten equations and solutions that appear to be from a mathematics exercise focusing on trigonometric identities and equations. ---Equation 21: The problem is:\[ 4\sin\theta - 1 = 2\sin\theta \]To solve for

Given: 4 sin(θ)-1=2 sin(θ) ⇒sin(θ)=2 sin(θ)+14 We have, sin(θ)=2 sin(θ)+14............(1) Substitute…

Answered: (21) 4sing-1 =2sine Sine=2sine+.

Trigonometry (MindTap Course List)

8th Edition

ISBN:9781305652224

Author:Charles P. McKeague, Mark D. Turner

Publisher:Charles P. McKeague, Mark D. Turner

Chapter2: Right Triangle Trigonometry

Section: Chapter Questions

Problem 5GP

See similar textbooks

Related questions

Topic Video

Question

100%

Find all solutions

The image contains handwritten equations and solutions that appear to be from a mathematics exercise focusing on trigonometric identities and equations.

---

Equation 21:

The problem is:

\[ 4\sin\theta - 1 = 2\sin\theta \]

To solve for $\sin\theta$:

\[ \sin\theta = \frac{2\sin\theta + 1}{4} \]

---

Next to the equations for Exercise 21, there are unrelated mathematical solutions without clear instructions:

\[ \frac{2\pi}{3} + 2\pi n \]

\[ \frac{\pi}{3} + \pi n \]

Equation 29:

Given:

\[ \tan 3x = \]

Solutions are partially visible:

\[ 3x = \frac{\pi}{6} \]

These sections are part of solving trigonometric equations to find the angles that satisfy the equation, given $\theta$ or $x$ in trigonometric functions. The letters $n$ typically denote any integer, suggesting multiple solutions based on periodic properties of trigonometric functions.

Expert Solution

Step 1

Given:

$4 \sin (θ) - 1 = 2 \sin (θ) \Rightarrow \sin (θ) = \frac{2 \sin (θ) + 1}{4}$

We have,

$\sin (θ) = \frac{2 \sin (θ) + 1}{4}$ ............(1)

Substitute $\sin (θ) = u$ in (1) we get,

$\Rightarrow u = \frac{2 u + 1}{4} Multiply by 4 both sides, \Rightarrow 4 u = 2 u + 1 Subtract 2u both sides, \Rightarrow 2 u = 1 Divide by 2 both sides, \Rightarrow u = \frac{1}{2}$

Step by step

Solved in 2 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Optimization$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.