Resources

Resources

Bytelearn - cat image with glasses

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.

7sin^(2)theta-3=4sin theta
Answer:
theta=

Find all angles, $0^{\circ} \leq \theta<360^{\circ}$ , that satisfy the equation below, to the nearest tenth of a degree. $\newline$ $7 \sin ^{2} \theta-3=4 \sin \theta$ $\newline$ Answer: $\theta=$

View step-by-step help

View step-by-step help

Find the roots of factored polynomials

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

7 \sin ^{2} \theta-3=4 \sin \theta

\newline

Answer:

\theta=

Rewrite Equation: Rewrite the given equation in a standard quadratic form. $\newline$ We have the equation $7\sin^2(\theta) - 3 = 4\sin(\theta)$ . To solve for $\theta$ , we need to rearrange the equation into a standard quadratic form, $ax^2 + bx + c = 0$ , where $x$ is $\sin(\theta)$ . $\newline$ $7\sin^2(\theta) - 4\sin(\theta) - 3 = 0$
Factor Quadratic: Factor the quadratic equation. $\newline$ We need to factor the quadratic equation $7\sin^2(\theta) - 4\sin(\theta) - 3 = 0$ . This can be done by looking for two numbers that multiply to give $-21$ ( $7 \times -3$ ) and add to give $-4$ . These numbers are $-7$ and $3$ . $\newline$ $(7\sin(\theta) + 3)(\sin(\theta) - 1) = 0$
Solve Factors: Solve each factor for $\sin(\theta)$ . We now have two factors that can be set to zero to solve for $\sin(\theta)$ : $7\sin(\theta) + 3 = 0$ or $\sin(\theta) - 1 = 0$ Solving each equation for $\sin(\theta)$ gives us: $\sin(\theta) = -\frac{3}{7}$ or $\sin(\theta) = 1$
Find $\sin(\theta) = -\frac{3}{7}$ : Find the angles that correspond to $\sin(\theta) = -\frac{3}{7}$ . $\newline$ Since $\sin(\theta) = -\frac{3}{7}$ does not correspond to a special angle, we will use a calculator to find the value of $\theta$ . We need to find the reference angle first and then determine the angles in the third and fourth quadrants where sine is negative. $\newline$ Reference angle = $\arcsin\left(\frac{3}{7}\right) \approx 25.4$ degrees $\newline$ Angles in the third and fourth quadrants: $180 + 25.4 = 205.4$ degrees and $360 - 25.4 = 334.6$ degrees
Find $\sin(\theta) = 1$ : Find the angles that correspond to $\sin(\theta) = 1$ . The angle where $\sin(\theta) = 1$ is a special angle, and we know that sine reaches its maximum value of $1$ at $\theta = 90$ degrees.
Compile Solutions: Compile all solutions. $\newline$ The angles that satisfy the original equation are approximately $205.4$ degrees, $334.6$ degrees, and $90$ degrees.

More problems from Find the roots of factored polynomials

Question

Find the degree of this polynomial.

\newline

`5b^{10} + 3b^3`

\newline

Posted 2 months ago

Question

\newline

(9a + 5) - (2a + 4)

\newline

Posted 2 months ago

Question

Find the product. Simplify your answer.

\newline

-3v^2(v^2 - 9)

\newline

Posted 1 month ago

Question

Find the product. Simplify your answer.

\newline

(v - 3)(4v + 1)

\newline

Posted 2 months ago

Question

Find the square. Simplify your answer.

\newline

(3y + 2)^2

\newline

Posted 2 months ago

Question

Divide. If there is a remainder, include it as a simplified fraction.

\newline

(24t^2 + 36t) \div 6t

\newline

Posted 2 months ago

Question

Is the function

q(x) = x^6 - 9

even, odd, or neither?

\newline

\newline

\text{[[even][odd][neither]]}

Posted 2 months ago

Question

Find the product. Simplify your answer.

\newline

-3q^2(-3q^2 + q)

\newline

Posted 2 months ago

Question

Find the product. Simplify your answer.

\newline

(r + 3)(4r + 2)

\newline

Posted 2 months ago

Question

Find the roots of the factored polynomial.

\newline

(x + 7)(x + 4)

\newline

Write your answer as a list of values separated by commas.

\newline

x =

Posted 2 months ago