Trigonometry Pile Up/Pythagoras?
http://www.greatmathsteachingideas.com/wp-content/uploads/2012/03/Trigonometry-Pile-Up1-724x1024.png Can you please help me, with the third from bottom triangle (pink/red)? If the side of the yellow triangle it shares, is 10.5cm? I know it involves pythagoras to work it out. (Trigonometry) Any other answers would be much appreciated.
Pythagorean identity trig hw help please?
a) well its pretty much just moving things around. so if you move the (2sin^2)(t) to the other side you get cos(2t) + (2sin^2)(t) = 1 then you can just subtract the cos(2t) then you get (2sin^2)(t) = 1 - cos(2t) b) same thing as part are just moving things around till you get the answer you need so move the one over 1 + cos(2t) = (2cos^2)(t) then you just subtract the cos(2t) (2cos^2)(t) - cos(2t) = 1 hope this helps is just basic algebra of moving variables around if it makes it easier turn the cos(2t) into x and 2cos^2(t) into y then just change it back later
Maths question. Pythagoras theorem & trig.?
No. Pretty much, what you do is do Pythagorean theorem on the two sides of the base of the cuboid - length and width. so, the diagonal of the base = sq. root of { 12^2 + 6^2 } = 13.416. Still, it's less than the needle, so we could see if placing the needle diagonally in the cuboid works. So, check the length of the base diagonal and the height of the needle. Length Available = sq. root of {13.416^2 + 4^2 } = 14 cm You need 15 cm for your needle to fit. So, nope. I hope you can understand what I'm saying - you really can't get too far on this one without a picture.
Who invented trigonometry and Pythagoras?
The field of trigonometry was a culmination of the works of many mathematicians over time, as most fields of mathematics are. However, the “father of trigonometry” is most often cited as Hipparchus.Hipparchus - WikipediaI am unsure of what you mean by who invented Pythagoras. Pythagoras of Samos was a Greek philosopher and mathematician most famously known for developing the Pythagorean Theorem.Pythagoras - Wikipedia
Trigonometric Identity-Pythagorean Identity Help?
You have a mistake in the line where you say you will replace with cos 2 sec^2 x(1 - sin^2 x) does not become 2 sec^2 x + cos^2 x ! it is 2 sec^2 x(cos^2 x) this can be simplified to [2/cos^2 x]cos^2 x which equals 2 Try to take it from there... One more hint - sin^2 x - cos^2 x = - (sin^2 x + cos^2 x) You can do it. Go for it. QED If you need more help, email me.
Algebra 2 Help: Pythagoras, Trigonometry, and Quadrants?
1) Simplify sine theta over square root of the quantity 1 minus sine squared theta. sin(x) / sqrt( 1- sin^2(x) ) = sin(x) / sqrt( cos^2(x) ) = sin(x) / cos(x) = tan Θ 2) Is square root 1 minus sine squared theta = cos Θ true? If so, in which quadrants does angle Θ terminate? It is true. The square root leads to a positive number. So the answer is in the quadrants where sine is positive. So (B) False True; quadrants I & IV True; quadrants II & III True; quadrants I & III 3) If sin Θ = 5 over 6, what are the values of cos Θ and tan Θ? cos(x) = +/- sqrt( 1 - sin^2(x) ) = +/- sqrt( 1 - 25/36 ) =+/- sqrt( 11/36 ) = ± sqt(11) / 6 tan(x) = sin(x) / cos(x) = +/- 5 / sqrt(11) cos Θ = ±11 over 36; tan Θ = ±1 over 11 cos Θ = ±square root 11 over 6; tan Θ = negative 1 over 11 cos Θ = ±11 over 6; tan Θ = negative 5 over 11 cos Θ = ±square root 11 over 6; tan Θ = ±5 square root 11 over 11 4) Simplify (1 − sin x)(1 + sin x). This is (a + b) (a - b) = a^2 - b^2 So this is 1 - cos^2(x) = sin^2(x) 1 cos2 x sin2 x tan2 x 5) If cos Θ = square root 2 over 2 and 3 pi over 2 < Θ < 2π, what are the values of sin Θ and tan Θ? If 3 pi over 2 < Θ < 2π Then the signs of sinx and tanx are both negative. cos(x) = sqrt(2)/2. So sin(x) = -sqrt(2)/2 and tan(x) = -1. sin Θ = square root 2 over 2; tan Θ = −1 sin Θ = negative square root 2 over 2; tan Θ = 1 sin Θ = square root 2 over 2; tan Θ = negative square root 2 sin Θ = negative square root 2 over 2; tan Θ = −1
Which is more accurate, Pythagoras' Theorem or Trigonometric Ratios?
For more accurate value comparatively apply here Pythagoras law instead of T- ratios….‘Coz by Pythagoras law , for calculating AB , you don't need any approximation..like AB = √(21² - 20²) = √(441 - 400) = √ 41 = 6.403… ( you may calculate up to any place)But if you calculate using T- ratio. ThenAB = sin12° * 21& here for calculating sin 12°, you need to use the approximate figures more than once…That means you are getting more & more away from the accurate value…So!!!! Use Pythagoras law… :)
What is the difference between trigonometry and Pythagoras theorem?
While Pythagoras theorem dealt with the relationship between the the three sides of a right angle triangle, trigonometry dealt with the relationship between the sides and the angles of right angle triangle.But for Pythagoras theorem, trigonometry wont have developed.
Why are we still teaching kids trigonometry and Pythagoras Theorem in the 21st Century?
The question of why we still teach the Pythagorean Theorem and what follows is easy. We want to move civilization forward, so we have to teach what we’ve learned so far, at least the important stuff. The Pythagorean Theorem is literally is the foundation for tons of math, including physics and many other application areas as well. As just one example, one way to write the equation for a spacetime interval in special relativity is[math]\Delta s^2 = \Delta x^2 + \Delta y^2 + \Delta z^2 - \Delta t^2[/math]It’s not exactly the Pythagorean Theorem; the negative sign puts a hyperbolic spin on the whole thing. But we really need to understand the Pythagorean Theorem first before we can understand this.The question about trigonometry is not why we teach it, but why we still teach it so poorly. High school trig has had a long, difficult trip from its beginnings as spherical astronomy to the tortured planar version we teach today. In this post I write about how trig starts from 1+1=2 and turns that into “an oddly notated squaring of two transcendental functions of a transcendental quantity representing a quarter of half a circle, said transcendental functions evaluating to irrational numbers.” That’s probably why it takes all year to teach two baby triangles, half an equilateral triangle and half a square, that the students already knew coming in.In many Quora answers I explore alternate approaches to trig. The most well-developed is Norm Wildberger’s Rational Trigonometry. N.J. gets all the transcendental functions and quantities out of trig, and does a good job getting many of the irrationals out as well. I like to answer Quora questions using it, which I imagine leaves most people wondering where I come up with these unusual formulas.I’ll just include a figure; check out my blog, which I hope to continue some day, for more information on Rational Trigonometry.