# Need help forgot how to do trig question

• hcky16
In summary, the conversation was about solving the equation 2(sin(x))^2+3sin(x)=-1 over the interval [0,2pi). The person asking for help showed their attempts at solving the equation and received feedback on how to correct their mistakes. The correct solutions for x were found to be x=pi/2, 5pi/6, and 13pi/6.
hcky16
I tried doing this problem but I don't think it is right can someone help me?
2(sin(x))^2+3sin(x)=-1 over the interval [0,2pi)

Show us what you've tried, and then we might be able to help you.

I tried,

2(sin(x))^2+3sin(x)=-1

2(sin(x))+3sin(x)+1=0

x=(-3(+/-)sqr 9-4(2)(1))/2(2)

x=(-3(+/-)1)/4

sinx=(-3(+/-)1)/4

x=arcsin(-3(+/-)1)/4

x=-90 or -30

x=-1.571 or -.524

hcky16 said:
I tried,

2(sin(x))^2+3sin(x)=-1

2(sin(x))+3sin(x)+1=0

x=(-3(+/-)sqr 9-4(2)(1))/2(2)

x=(-3(+/-)1)/4
There's a typo in the 2nd line, and the last two lines aren't technically correct. You need to put the "sin" in front of the x. Also, you really didn't need to use the quadratic formula. This expression on the LHS:
$$2\sin^2 x + 3\sin x + 1 = 0$$
is factorable.

sinx=(-3(+/-)1)/4

x=arcsin(-3(+/-)1)/4

x=-90 or -30

x=-1.571 or -.524
Some problems here. First, these answers are not in the interval [0, 2pi). Just add 2pi to these answers and you'll be okay.

Second, the range of the arcsin function is only [-pi/2, pi/2], so there are actually 3 solutions that I see, not 2. (There is another angle whose sin is -1/2.)

The question asks you to find the solution in [0,2pi). The answer you report is not.
For what value of x in [0,2pi) is sin(x) = -1 OR -1/2?

## 1. What is trigonometry and why is it important?

Trigonometry is a branch of mathematics that deals with the study of triangles and their relationships. It is important because it is used in various fields such as physics, engineering, and navigation to solve problems involving angles and distances.

## 2. How do I solve a trigonometry problem?

To solve a trigonometry problem, you need to identify the given information, draw a diagram, and apply the appropriate trigonometric ratio (sine, cosine, or tangent) to find the missing side or angle. It is important to remember the trigonometric identities and formulas to simplify the problem.

## 3. What are the trigonometric ratios and how are they used?

The trigonometric ratios are sine, cosine, and tangent, which are abbreviated as sin, cos, and tan. These ratios are used to find the relationship between the sides and angles of a right triangle. Sine is the ratio of the opposite side to the hypotenuse, cosine is the ratio of the adjacent side to the hypotenuse, and tangent is the ratio of the opposite side to the adjacent side.

## 4. What is the Pythagorean theorem and how is it related to trigonometry?

The Pythagorean theorem states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides in a right triangle. This theorem is related to trigonometry because it can be used to find the missing side in a right triangle when the other two sides are known.

## 5. What are some real-world applications of trigonometry?

Trigonometry is used in many real-world applications, such as calculating the height of a building or mountain, finding the distance between two objects, and determining the angle of elevation or depression. It is also used in fields like architecture, surveying, and astronomy to make accurate measurements and calculations.

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