th Trying trig Everything you need to Know By: Noah Gregory subject Page Radians & Degree Measure 3 Unite Circle 4 Right Triangle Trig 5-7 trig functions of any angle 8-10 graphs 11-15 using fundamental trig identities 16-17 verifying trig identities 18-20 solving trig equations 21-23 sum & difference formulas 24 law of sines 25-27 laws of cosines 28-29 vectors 30-31
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− + − Geometric series 1 for 1 1 (1 ) 1 = − < − = − = ∞ − r r S a r S a r u ar n n n n Summations ( )1 2 1 1 + = Σ= r n n n r ( 1)(2 1) 6 1 1 2 + + = Σ= r n n n n r 2 2 4 1 1 3 ) 1 ( + = Σ= r n n n r Trigonometry – the Cosine rule a2 = b2 + c2 − 2bc cos A Binomial Series ∈ + + ⎟ ⎟⎠ ⎞ ⎜ ⎜⎝ ⎛ + + ⎟ ⎟⎠ ⎞ ⎜ ⎜⎝ ⎛ + ⎟ ⎟⎠ ⎞ ⎜ ⎜⎝ ⎛ + = + − − a − b b n r n a b n a b n a b n an n n n r r n ( 2 1 ( ) 1 2 2 … … ) where !( )! C ! r n
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Project in Math Chapter 6 Circular Functions and Trigonometry Submitted to: Mrs. Velasco Submitted by: Angelo Jet Manarin IV – Bravo Angles & Their Measures A definition of an angle would be that an angle is the union of two rays that have the same endpoint. The sides of the angles are the two rays, while the vertex is their common endpoint. stands for an angle. You can put it in front of three letters which represent points. The first and third letters represent points on each of the rays
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(b2 – 4ac) x = –––––––––––––– . 2a Binomial Theorem (a + b)n = an + (n) a 1 n – 1b + (n) a 2 n – 2b2 +…+ ( nr ) a n – r br + … + b n, where n is a positive integer and –––––––– ( nr ) = (n –n! r! . r)! 2. TRIGONOMETRY Identities sin2 A + cos2 A = 1. sec2 A = 1 + tan2 A. cosec2 A = 1 + cot2 A. Formulae for ∆ ABC c b a –––– = –––– = –––– . sin A sin B
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How to Succeed in Physics (and reduce your workload) Kyle Thomas, Lead Author Luke Bruneaux, Supporting Author Veritas Tutors, LLC How To Succeed in Physics | 2 About the Authors Kyle Thomas Kyle is currently a PhD candidate in the Psychology Department at Harvard University where he studies evolutionary social psychology and serves as a teaching fellow for graduate and undergraduate courses. Kyle has primarily tutored and taught Physics and Organic Chemistry through the UC Santa
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of engineering tasks and will provide a base for further study of engineering mathematics. • Unit abstract This unit enables learners to develop previous mathematical knowledge obtained at school or college and use fundamental algebra, trigonometry, calculus, statistics and probability for the analysis, modelling and solution of realistic engineering problems. Learning outcome 1 looks at
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Right Triangles Word Problems with Illustrations and Solutions 1. Solve the right triangle ABC given that c = 18 cm and b = 9 cm. To find the remaining side a, use the Pythagorean Theorem: a2 + b2 = c2 a2 = c2 - b2 a2 = (18cm)2-(9cm)2 a2 = 324cm2 – 81cm2 a2 = 243cm2 a = 15.59cm 2. Ben and Emma are out flying a kite. Emma can see that the kite string she is holding is making a 70° angle with the ground. The kite is directly above Ben, who is standing 50 feet away. To the nearest foot, how many
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c 2012 Math Medics LLC. All rights reserved. TRIGONOMETRIC IDENTITIES • Reciprocal identities 1 1 sin u = cos u = csc u sec u 1 1 tan u = cot u = cot u tan u 1 1 csc u = sec u = sin u cos u • Pythagorean Identities sin2 u + cos2 u = 1 1 + tan2 u = sec2 u 1 + cot2 u = csc2 u • Quotient Identities sin u cos u tan u = cot u = cos u sin u • Co-Function Identities π π sin( − u) = cos u cos( − u) = sin u 2 2 tan( csc( π π − u) = cot u cot( − u) = tan u 2 2 sec( π − u) = csc u 2 • Sum-to-Product Formulas
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The graphs of the sine and cosine functions Let's continue to use t as a variable angle. A good way for human beings to understand a function is to look at its graph. Let's start with the graph of sin t. Take the horizontal axis to be the t-axis (rather than the x-axis as usual), take the vertical axis to be the y-axis, and graph the equation y = sin t. It looks like this. First, note that it is periodic of period 2. Geometrically, that means that if you take the curve and slide it 2 either
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1. N/a 2. using Law of Sines and Law of Cosines. You get two different triangles. The one combination you can't have is where A is opposite the b. Maybe your notation already specifies this, but I don't think so, otherwise there is no problem. If you try to construct a triangle with the 70 degree angle opposite the side of length 5, the Law of Sines would give sin x = (7/5)sin 70 = 1.316, which is impossible. With angle A = 70 opposite the side of length 7, the Law of Sines gives sin x = (5/7)sin
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