Find all angles, 0^(@) <= theta < 360^(@), that satisfy the equation below, to the nearest tenth of a degree. 2sin^(2)theta-2sin theta=-3sin theta+1 Answer: theta=

Rewrite Equation: Rewrite the given equation to collect like terms on one side. 2sin^2(theta) - 2sin(theta) + 3sin(theta) - 1 = 0Simplify Equation: Simplify the equation by combining like terms. 2sin^2(theta) + sin(theta) - 1 = 0Factor Quadratic: Factor the quadratic equation in terms of sin(theta). (2sin(theta) - 1)(sin(theta) + 1) = 0Set Factors Equal: Set each factor equal to zero to find the values of sin(theta). 2sin(theta) - 1 = 0 or sin(theta) + 1 = 0Solve for sin(theta): Solve each equation for sin(theta). For 2sin(theta) - 1 = 0: sin(theta) = 1/2 For sin(theta) + 1 = 0: sin(theta) = -1Find sin(theta) = 1/2: Find the angles theta that correspond to sin(theta) = 1/2 between 0 degrees and 360 degrees. sin(theta) = 1/2 at theta = 30 degrees and theta = 150 degrees.Find sin(theta) = -1: Find the angles theta that correspond to sin(theta) = -1 between 0 degrees and 360 degrees. sin(theta) = -1 at theta = 270 degrees.Combine Solutions: Combine the solutions from steps 6 and 7 to list all the angles that satisfy the original equation. theta = 30 degrees, 150 degrees, and 270 degrees.

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Find all angles,
0^(@) <= theta < 360^(@), that satisfy the equation below, to the nearest tenth of a degree.

2sin^(2)theta-2sin theta=-3sin theta+1
Answer:
theta=

Find all angles, 0^{\circ} \leq \theta<360^{\circ} , that satisfy the equation below, to the nearest tenth of a degree. $\newline$ $2 \sin ^{2} \theta-2 \sin \theta=-3 \sin \theta+1$ $\newline$ Answer: $\theta=$

View step-by-step help

Home

Math Problems

Algebra 2

Csc, sec, and cot of special angles

Full solution

Q. Find all angles,

0^{\circ} \leq \theta<360^{\circ}

, that satisfy the equation below, to the nearest tenth of a degree.

\newline

2 \sin ^{2} \theta-2 \sin \theta=-3 \sin \theta+1

\newline

Answer:

\theta=

Rewrite Equation: Rewrite the given equation to collect like terms on one side. $\newline$ $2\sin^2(\theta) - 2\sin(\theta) + 3\sin(\theta) - 1 = 0$
Simplify Equation: Simplify the equation by combining like terms. $2\sin^2(\theta) + \sin(\theta) - 1 = 0$
Factor Quadratic: Factor the quadratic equation in terms of $\sin(\theta)$ . $\$2\sin(\theta) - 1)(\sin(\theta) + 1) = 0$
Set Factors Equal: Set each factor equal to zero to find the values of $\sin(\theta)$ . $2\sin(\theta) - 1 = 0$ or $\sin(\theta) + 1 = 0$
Solve for $\sin(\theta)$ : Solve each equation for $\sin(\theta)$ . For $2\sin(\theta) - 1 = 0$ : $\sin(\theta) = \frac{1}{2}$ For $\sin(\theta) + 1 = 0$ : $\sin(\theta) = -1$
Find $\sin(\theta) = \frac{1}{2}$ : Find the angles $\theta$ that correspond to $\sin(\theta) = \frac{1}{2}$ between $0$ degrees and $360$ degrees. $\newline$ $\sin(\theta) = \frac{1}{2}$ at $\theta = 30$ degrees and $\theta = 150$ degrees.
Find $\sin(\theta) = -1$ : Find the angles $\theta$ that correspond to $\sin(\theta) = -1$ between $0$ degrees and $360$ degrees. $\newline$ $\sin(\theta) = -1$ at $\theta = 270$ degrees.
Combine Solutions: Combine the solutions from steps $6$ and $7$ to list all the angles that satisfy the original equation. $\newline$ $\theta = 30$ degrees, $150$ degrees, and $270$ degrees.