# Find exact solutions on the interval [0, 2pi) of 10sin^2+7sin+1=0

1 answer

###### Question:

Find exact solutions on the interval [0, 2pi) of 10sin^2+7sin+1=0

## Answers

[tex]\bf \stackrel{\stackrel{\textit{notice is just}\qquad ax^2+bx+c=0}{\downarrow }}{10sin^2(\theta )+7sin(\theta )+1}\implies [5sin(\theta )+1][2sin(\theta )+1]=0 \\\\[-0.35em] ~\dotfill\\\\ 5sin(\theta )+1=0\implies 5sin(\theta )=-1\implies sin(\theta )=-\cfrac{1}{5} \\\\\\ \theta =sin^{-1}\left(-\cfrac{1}{5} \right)\implies \theta \approx \begin{cases} 191.54^o\qquad &III~Quadrant\\ 348.46^o\qquad &IV~Quadrant \end{cases} \\\\[-0.35em] ~\dotfill[/tex][tex]\bf 2sin(\theta )+1=0\implies 2sin(\theta )=-1\implies sin(\theta )=-\cfrac{1}{2} \\\\\\ \theta =sin^{-1}\left( -\cfrac{1}{2} \right)\implies \theta = \begin{cases} 210^o\qquad &III~Quadrant\\ 330^o&IV~Quadrant \end{cases}[/tex]recall sine is negative on the III and IV Quadrants only.

#### Similar Solved Questions

1 answer

### How many grams of the reactant in excess will remain after the reaction?

How many grams of the reactant in excess will remain after the reaction?...

1 answer

### Brainliest for the correct awnser!! A calculator was used to perform a linear regression on the values in the table. The results are shown to the right of the table.What is the line of best fit?A.y = –0.984x + 13.5B.y = –2.9x + 13.5C.–0.984 = –2.9x + 13.5D.y = 13.5x – 2.9

Brainliest for the correct awnser!! A calculator was used to perform a linear regression on the values in the table. The results are shown to the right of the table.What is the line of best fit?A.y = –0.984x + 13.5B.y = –2.9x + 13.5C.–0.984 = –2.9x + 13.5D.y = 13.5x – 2.9...

1 answer

### Eric and Shiloh each have a savings account. The ratio of Eric’s account balance to Shiloh’s account balance is 4:3. Together they have a total of $140 in their accounts. Use the tape diagram below to help you determine the balance of Eric’s account. [Type your answer as a number.] FYI: there are seven bars down below, i dunno how to put the pictures there bc im on comupter

Eric and Shiloh each have a savings account. The ratio of Eric’s account balance to Shiloh’s account balance is 4:3. Together they have a total of $140 in their accounts. Use the tape diagram below to help you determine the balance of Eric’s account. [Type your answer as a number.]
FYI: ther...

2 answers

### Shondra was unsure about what career to go into. Her high school counselor suggested a personal assessment to point out Shondra’s interests. The assessment revealed that Shondra is very passionate about justice and making sure that people stay safe and treat each other fairly. Shondra also enjoys physical fitness and can handle risky high-pressure situations well. Shondra would be well suited for which career cluster. Select three options. law security education public safety physical education

Shondra was unsure about what career to go into. Her high school counselor suggested a personal assessment to point out Shondra’s interests. The assessment revealed that Shondra is very passionate about justice and making sure that people stay safe and treat each other fairly. Shondra also enjoys ...

1 answer

### Explain whether your breakfast was a compound, homogeneous mixture, or heterogenous mixture.

Explain whether your breakfast was a compound, homogeneous mixture, or heterogenous mixture....

1 answer

### (_2/3)(Raised to power 3) multiplied by (_3/2)(raised to power 2)

(_2/3)(Raised to power 3) multiplied by (_3/2)(raised to power 2)...

2 answers

### Which definition best describes an adjective?

which definition best describes an adjective?...

1 answer

### Answer the following in several complete sentences: A college professor wants to measure memory in elementary students before a vocabulary quiz. How could she operationally define memory? (pls give a genuine answer with an operational definition or just dont answer)

Answer the following in several complete sentences:
A college professor wants to measure memory in elementary students before a vocabulary quiz. How could she operationally define memory?
(pls give a genuine answer with an operational definition or just dont answer)...

2 answers

### More than ___________ percent of the people killed in alcohol-related crashes in the US were drivers with a B.A.C of .08 or higher.

More than ___________ percent of the people killed in alcohol-related crashes in the US were drivers with a B.A.C of .08 or higher....

1 answer

### Make a lengthy note on AEROBIC and ANA-AEROBIC respiration,include equations where necessary and feel free to add pictures. Please never forget my rule, don't give me a guess work and always make researches when you are not sure. Love you all, take your time!!!.Time to see geniuses, don't feel bad if you don't answer because you are still the best.

Make a lengthy note on AEROBIC and ANA-AEROBIC respiration,include equations where necessary and feel free to add pictures. Please never forget my rule, don't give me a guess work and always make researches when you are not sure. Love you all, take your time!!!.Time to see geniuses, don't feel bad i...

1 answer

### Explain how the Mexican-American war started

Explain how the Mexican-American war started...

2 answers

### The figure is made up of a cylinder and a hemisphere. To the nearest whole number, what is the approximate volume of this figure? Use 3.14 to approximate π .

The figure is made up of a cylinder and a hemisphere.
To the nearest whole number, what is the approximate volume of this figure?
Use 3.14 to approximate π ....

1 answer

### Over the next three years, the expected path of 1-year interest rates is 4, 1, and 1 percent. The expectations theory of the term structure predicts that the current interest rate on 3-year bond is _____.(a) 1 percent.(b) 2 percent.(c) 3 percent.(d) 4 percent.(e) 5 percent.

Over the next three years, the expected path of 1-year interest rates is 4, 1, and 1 percent. The expectations theory of the term structure predicts that the current interest rate on 3-year bond is _____.(a) 1 percent.(b) 2 percent.(c) 3 percent.(d) 4 percent.(e) 5 percent....

1 answer

### How the intestinal cells help the intestines work within the digestive system

how the intestinal cells help the intestines work within the digestive system...

1 answer

### Pls help me with b and c. Also, use the 1/2 cup over 1/8 cup too for the answer and question. It is 25 points if you answer.

Pls help me with b and c. Also, use the 1/2 cup over 1/8 cup too for the answer and question. It is 25 points if you answer....

2 answers

### At James’s funeral, his sister spoke to the hundreds of people who came to pay their last respects. She said, “My brother James was a man who did his best at what he loved to do. He was rewarded with medals, trophies, awards, and money. Yet, he died alone and without a friend in the world.” The tone of the funeral speech is one of a Hopelessness b Sadness c Optimism d Joy

At James’s funeral, his sister spoke to the hundreds of people who came to pay their last respects. She said, “My brother James was a man who did his best at what he loved to do. He was rewarded with medals, trophies, awards, and money. Yet, he died alone and without a friend in the world.”
Th...

1 answer

### A recent study by Rover.com surveyed a random sample of 1500 dog owners. The research revealed that 975 of the dog owners admit to taking more photos of their dog than their significant other. Which of the following gives a 95% confidence interval for the proportion of all dog owners that would admit to taking more photos of their dog than their significant other? (A) 0.65 = 1.96, 0.65(0.35) (B) 0.65 +2.5 0.65(0.35) 1500 (C) 0.65 +1.96-1660 (D) 975 +2.576-975 (E) 975 + 1.96 975(625 Submit Answer

A recent study by Rover.com surveyed a random sample of 1500 dog owners. The research
revealed that 975 of the dog owners admit to taking more photos of their dog than their
significant other. Which of the following gives a 95% confidence interval for the proportion
of all dog owners that would admi...