- #1
hcky16
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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)
2(sin(x))^2+3sin(x)=-1 over the interval [0,2pi)
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: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
Some problems here. First, these answers are not in the interval [0, 2pi). Just add 2pi to these answers and you'll be okay.sinx=(-3(+/-)1)/4
x=arcsin(-3(+/-)1)/4
x=-90 or -30
x=-1.571 or -.524
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.
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.
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.
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.
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.