Do you know some APPLICATION PROBLEMS dealing with oblique triangles and trigonometric identities?
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The trigonometric identities have as their primary purpose to simplify calculations.  For example, why evaluate 2sinxcosx when you can evaluate sin2x.\n\nAs for the applications, oblique triangles are used in surveying and mapping.  For example, suppose you want to know your distance from an object on the opposite side of a river.  You can mark off a line of a fixed distance, say 100ft.  Then, go to the opposite ends of the line and use a transit to measure the angle between the object and the line you measured.  You can now determine all three sides with this information.
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sin(A+B)sin(A-B)/(cos²Acos²B)\n= (sinAcosB + cosAsinB)(sinAcosB - cosAsinB)/(cos²Acos²B)\n= (sin²Acos²B - cos²Asin²B)/(cos²Acos²B) (since (x + y)(x - y) = x² - y²)\n= sin²A/cos²A - sin²B/cos²B\n= tan²A - tan²B ← Option c)\n\nPlease note: sin(A + B) = sinAcosB + cosAsinB\nand sin(A - B) = sinAcosB - cosAsinB
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Fermat's Last Theorem has been solved ashas the Four Color Theorem. The Poincare conjecture has recently been solved. Trisecting a general angle with unmarked straightedge and compass has been shown to be unsolvable (although it is possible with marked straightedge and compass).\n\nHigh on the list of open problems:\n\nRiemann Hypothesis.\nP=NP?\nTwin prime conjecture.\nAre there any odd perfect numbers?\nProof of existence of solutions to Navier-Stokes equations.
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The Pythagorean theorem only works with right triangles.  Try using SIN, COS or TAN.
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Come on, this is an EASY one.\n\nHere's how you do identities in general.  Look to see what the differences are in the two sides.  Then, look for an identity that can fix those differences.\n\nFor example, the main difference between the left and right side is, there is sin^2 on the left, but not on the right.  So somehow, the sin^2 has to disappear.  Additionally, there are only cos^2's on the right, so whatever you do you your sin^2, it has to turn into some form of cos^2.\n\n\n\nAre you GETTING this?\n\n\n\n\nStart with the left side.  Replace sin^2 (theta) with 1 - cos^2 (theta).  Do the algebra that ensues to get the right side.
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With these data a lot of angles fulfill that requirement; If  you have alpha first look at cos alpha, after divide by1.33  and look for theta.\n\nDid you not make a mistake. I suppose you mean sin and not cos\n\nSnell law uses sinus
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Remember the definitons of tangent, cotangent, etc. as they relate to right triangles.  Draw a triangle for both α and β.  Use the pythagorean theorem to finr the hypotneuses.  You will find the sides of the α triangle to be 3, 4, 5.  so:\n\nsin α = 4/5\ncos α = 3/5\n\nDo the same for β and the triangle is 5, 12, 13 with:\n\nsin β = 12/13\ncos β = 5/13\n\nFinaly, use the identity:\n\n sin(α-β) = sin α  cos β - sin β cos α \n\nSubstituting:\n\nsin(α-β) = (4/5)(5/13) - (12/13)(3/5) = (20 - 36)/65 = - 16/65
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my school asked us to do just one: the daily applications of geometry (with special emphasis on Similar Triangle, Trig and Pyth theorem)
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On the calc. you'll see SIN, COS, and TAN\n\nSin- Sine\nCos- Cosine\nTan- Tangent\n\n\nAll used for trigonometry.
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Are you looking for someone to do your homework?\nGeometry is very simple. There are three basic shapes, The sphere, Triangle and the Square. Learn that a circle is nothing more than a shadow of a sphere and that shadow is but a line. The angle is your point of view. To solve for X you must know two of the three. X is only unknown for a very short time. There are 10 dimensions. Length, width, height, area, volume, weight, mass, velocity, time, and infinity. Any math problem may be solved if two or more dimensions are known. The lowest common denominator is two and if two of anything is known the third dimension will be also known.\nie. a triangle with equal sides is composed of 3, 60 degree angles, 60 + 60 + 60 = 180 degrees. Knowing that half of a circle which is half of a sphere multiply by the common denominator of 2 and 360 appears which is a sign for infinity, through in any of the dimensions given  such as volume, mass, velocity, etc. any problem can be solved. Linear problems are solved with the triangle also. For every side there is the other. Make the triangle square or draw a square and divided it in two by a linear line from the opposing corner. Solve the problem L x W x H and you have area. Divide the area of the square by two and you have the area of the triangle. Pi is infinity, in math it is 3.14 and then some. Pi is also the Greek word for the Egyption (word) hieroglift of the lazy 8 which is a symbol for infinity also, it is a mineral we call magnetite. Magnetite in crystal form is in the shape of tetrahedron which we know as a pyramid times 2. The numeral 8 is an Aribic number which means 4 + 4. It is not of any quincedence that a pyramid has four faces. The mystery of the pyramids has been solved by Paul Einstein. Geometry is fun if you know how it came to be.
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Trignometry could be made interestingly easy.\nUnderstand the basics:\nThe longest side of triangle is hypotenuse.\nThe side of the triangle opposite the angle(your angle) is the perpendicular.\nthe remaining side is called the base.\n\nsine theta=perpendicular/hypotenuse\ncosine theta=base/hypotenuse\ntangent theta=sine theta/cos theta=perpendicular/base\n\nAll other formulas are based on these relationships.\nlike sine square theta+cosine square theta=1 etc.
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The faster way to solve this questions is using graphical method. Draw the respective triangles (choosing appropriate scale) and you will get answer.
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So you know the ones for sin(2a) and cos(2a). Cool.\n\nNow, tan(2a) is the same as sin(2a)/cos(2a), since tan = sin/cos (definition of tangent).\n\nSub in the formulae for sin(2a) and cos(2a) :\n\n2sin(a)cos(a)\n----------------\ncos(a)^2-sin(a)^2\n\nDivide both numerator and denominator by (cos(a))^2\n\n2tan(a)\n----------\n1-tan(a)^2
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sin(2x) = 2sinxcosx is a trigonometric identity called the double angle identity. It was derived from another identity:\n\n   sin(x + y) = sinxcosy + cosxsiny\n \nhere x and y are two different angles but what if x = y\nreplace y with x to make all the equations in terms of x, thus the equation becomes:\n\n   sin(x + x) = sinxcosx + cosxsinx\n   \nnote that sinxcosx is also equal to cosxsinx, so simplifying the equation it becomes:\n\n  sin(2x) = 2sinxcosx or sin(2x) = 2cosxsinx
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oblique, obilisque shape
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Depending on what you need to solve, you need two angles and a side, or two sides and an angle. Hit me with an E-Mail if you are stuck with something.\n\nkeptcompany@yahoo.com
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it's "pi" not "pie" dear ... :-)\n\nAnd, yes I do know how to prove those identities.\n\nAnd, no I won't do them all, as it will deprive you of the wonderful opportunity to learn and practice for your test. \n\nBut, I will do one for you!  I'll do #8:\n\n(sinx + cosx) ² =\nsin²x + 2sinxcosx + cos²x = \nsin²x + cos²x + 2sinxcosx = \n1 + 2sinxcosx  {{ using trig ID #1 }} = \n1 + sin2x {{ using trig ID #2 }}\n. . . . .\nTrig ID #1 :  sin²x + cos²x = 1\nTrig ID #2 :  sin2x = 2sinxcosx\n\nNRT