The solution set of the inequality sin x sqrt(3)cos x 0 is

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The solution set of the inequality sin x sqrt(3)cos x 0 is

Gerd Altmann/Pixabay If you're trying to figure out what x squared plus x squared equals, you may wonder why there are letters in a math problem. That's because, in the case of an equation like this, x can be whatever you want it to be. To find out what x squared plus x squared equals, you have to multiply x times itself. Then you add that number to itself to get your final answer.Examples of X Squared Plus X Squared Here are some examples of that equation to make it easier to understand. If x equals 2, then x squared, or x times itself, equals 4. Add four to itself, and you get 8. Therefore, 2 squared plus 2 squared equals 8. To use another example, let's see what happens when x equals 3. In that case, x squared equals 9. Then, 9 plus 9 equals 18. The beauty of this equation is that x can equal anything, and you can solve it using whatever value you want for x. Math that Uses Letters We call mathematics that uses letters to take the place of different values algebra. Algebra uses symbols in most cases, letters to represent quantities that don't necessarily have the same value all the time. These quantities are called variables, and you can figure out what those variables mean when you use algebra. Equations are like sentences that explain the relationships between numbers and variables. You figure out what the variables in an equation are by solving it. When you solve an equation in algebra, you break it down to its simplest form and discover what the variables mean. A Brief History of Algebra Since ancient times, mathematicians have worked with unknown variables in different ways. Islamic scholars began to give the science of working with variables a name. They called this type of math the "science of restoration and balancing," and the Arabic word for "restoration," or "al-jabru," became the root word for the word "algebra." As mathematicians in the Middle Ages experimented with the principles of algebra, they realized they could solve equations for two- and three-dimensional items, which led to even more discoveries of what algebra could do. Modern scholars have found even more complex equations that algebra can solve. Algebra in Everyday Life You may have heard people say that you'll never use algebra in your everyday life, but you'd be surprised at how often you use algebra. Algebra comes in handy when you're trying to figure out how much a group of items costs per item. When you're trying to figure out how to split a restaurant bill or how much gas you can buy for a certain amount. You can use algebra to figure out the dimensions of a room or even as you make up your shopping list. Algebra is a versatile form of math that you use more often than you might think and, sometimes, you don't even realize that you're solving math problems. Why It's Important to Learn Algebra Learning algebra is important for more than just solving equations. Educators consider algebra the gateway to higher forms of math, so if you or your child wants to explore a career in science or technology, algebra can unlock so many more new ideas. Algebra can also help students with critical thinking and logic skills. Using algebra is like exercise that helps make your brain stronger. Putting algebra to use in your everyday life can help you in so many ways. MORE FROM Divide each term in the equation by .Replace with an equivalent expression in the numerator.Rewrite in terms of sines and cosines.Apply the distributive property.Cancel the common factor of .Cancel the common factor.Add to both sides of the equation.Take the inverse tangent of both sides of the equation to extract from inside the tangent.The tangent function is positive in the first and third quadrants. To find the second solution, add the reference angle from to find the solution in the fourth quadrant.To write as a fraction with a common denominator, multiply by .Write each expression with a common denominator of , by multiplying each by an appropriate factor of .Combine the numerators over the common denominator.The period of the function can be calculated using .Replace with in the formula for period.The absolute value is the distance between a number and zero. The distance between and is .The period of the function is so values will repeat every radians in both directions., for any integer Consolidate the answers., for any integer OK, sure, the name of this cocktail has a naughty Christmas sort of vibe. But that doesn't mean you can't sip this steamy drink all throughout the colder months, enjoying the pick-me-up hint of coffee paired with the rich bite of Armagnac. 1 1/2 ounces Ch?teau de Laubade XO Bas Armagnac 1/2 ounce chestnut liqueur 1/2 ounce coffee liqueur 1/2 ounce g?n?py liqueur 5 coffee beans 2 1/2 ounces hot water Garnish: grated nutmeg In a small saucepan, combine all of the ingredients except for the water, and heat without bringing to a boil. Strain the mixture into a toddy glass, and top with hot water to fill. Rate This Recipe I don't like this at all. It's not the worst. Sure, this will do. I'm a fan--would recommend. Amazing! I love it! Thanks for your rating! VerifiedHint: In this question, we first need to divide both the sides with 2. Then write the constant terms in terms of trigonometric ratios of some known angles of sine and cosine. Now, use the trigonometric ratios of compound angles formula and convert it to sine function. Then using the inequality we get the value of x.\[\sin \left( A+B \right)=\sin A\cos B+\cos A\sin B\]Complete step-by-step answer:Now, from the given inequality in the question we have,\[\Rightarrow \sin x+\sqrt{3}\cos x>0\]Let us now divide with 2 on both the sides\[\Rightarrow \dfrac{1}{2}\sin x+\dfrac{\sqrt{3}}{2}\cos x>0\]As we already know that\[\cos \dfrac{\pi }{3}=\dfrac{1}{2},\sin \dfrac{\pi }{3}=\dfrac{\sqrt{3}}{2}\]Now, let us write the constant values in terms of standard values mentioned above\ [\Rightarrow \sin x\cos \dfrac{\pi }{3}+\cos x\sin \dfrac{\pi }{3}>0\]As we already know that from the trigonometric ratios of compound angles formula that\[\sin \left( A+B \right)=\sin A\cos B+\cos A\sin B\]By, using this formula the above inequality can be converted as\[\Rightarrow \sin \left( x+\dfrac{\pi }{3} \right)>0\]As we already know that the sine function is positive in the first and second quadrants we can get the value of the angle where it lies,Now, sine function is positive for the angles\[\Rightarrow 0

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