Log 3 2cos 2x 3cosx

    • [PDF File]Trig Equations with Half Angles and Multiple Angles angle

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      2cos 2x 1 cos x 0 2cos 2x cos x 1 0 2cos x 1 cos x 1 0 Now divide the the problem into two parts 2cos x 1 0 or cos x 1 0 cos x 1 2 or cos x 1 x 3 or x 5 3 or x The solution set is S.S. 3, , 5 3 Example : Solve 1 sin cos2 over the interval 0°,360° . Solution : Replace cos2 using a double-angle identity. 1 sin cos2 1 sin 1 2sin 2

    • [PDF File]SOLUTIONS TO USC’S 2004 HIGH SCHOOL MATH CONTEST

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      SOLUTIONS TO USC’S 2004 HIGH SCHOOL MATH CONTEST 1. (d) Observe that BCis the height of 4ABD with base AD.Hence, the area of 4ABD is (1=2) 3 6=9. 2. (e) Square both sides of the equation p 3−x + p 3+x=xto obtain 6+2 p 9−x2=x2.It is easy to see that x =2 p 2= p 8is a solution. To solve for x, one can square both sides of 2 p

    • [PDF File]Discussion 20 Worksheet Answers - University of California, Berkeley

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      x= 0 and x= 3 z. 2.Compute RR S (r F~)dS~where F~= (y; x;yx3) and Sis the portion of the sphere of radius 4 with z 0 and the upwards orientation. 3.Compute RR S F~dS~ where F~ = (sin(ˇx);zy3;z2 + 4x) where S is the surface of the box 1 x 2, 0 y 1, and 1 z 4, oriented outwards. Solution: 1.Parametrize the surface by x= x, y= 2cos , and z= 2sin ...

    • [PDF File]Pre-Calculus Name Amplitude = Amplitude = Amplitude= 2 4 cos 5x 9. y ...

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      20. y = –2 sin(–2x) Amplitude = _____ Period = _____ 21. Find an equation for a sine function that has amplitude of 4, a period of π. 22. Find an equation for a cosine function that has an amplitude of 3 5, a period of 3 2 π. 23.

    • [PDF File]Chapter 7: Trigonometric Equations and Identities - OpenTextBookStore

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      2sin 1T 2cos 1 2. 2sin € 3 T 3. T 4. 2cos € 2 Find all solutions. 5. 2sin 1€ 4 x §·S ¨¸ ©¹ 6. 2sin €2 3 x §·S ¨¸ 7. 2cos 2 €3 t 8. 2cos 3 1t 9. 3cos €2 5 x §·S ¨¸ ©¹ 10. 8cos 6 2 x §·S ¨¸ 11. 7sin 3 2 t 12. 4sin 4 1 t Find all solutions on the interval [0,€2 )S. 13. 10sin cos 6cosx x x 3sin 15cos sin 14. t t t ...

    • [PDF File]Math 417 – Midterm Exam Solutions Friday, July 11, 2008

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      (a) log(3− 4i) (b) (2+2i)i Solution: (a) The modulus of z = 3 − 4i is r = 5 and the principal argument is Θ = tan−1 − 4 3 . Therefore, the values of log(3−4i) are logz = lnr +i(Θ +2kπ) log(3−4i) = ln5+ i tan−1 − 4 3 +2kπ where k = 0,±1,±2,.... (b) The values of (2+2i)i are obtained using the formula (2+2i) i= e log(2+2 )

    • [PDF File]Exam 3 - Mathematics

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      3. Checking the signs of the second derivative, we find thatf′′(x) > 0 on (−∞,−4/ √ 3) and on (4/ √ 3,∞) so it is concave up there. It is concave down on the interval (−4/ √ 3,4/ √ 3). (c)Find the points that give local maximum values of f(x), the points that give local minimum values of f(x), and the points of inflection ...

    • [PDF File]Compound Trigonometric Function Worksheet Names page 1 of 3 ...

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      * R. Greenlee Wheaton Warrenville South High School, Wheaton Il. 07/27/00 * Compound Trigonometric Function Worksheet continued page 2 of 3 ΙΙ. Changing the phase shift 'c' while keeping 'a', and 'b' the same:

    • [PDF File]www.pioneermathematics.com MOBILE : 9815527721, 4617721 PIONEER GUESS ...

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      x y z x y z 9 6x 8y 16 25 10z 1 2x 9 6y 49 14z2 2 2 2 2 2+ + + + + + − − + + − + + + − + + =2k 2. L.K. Gupta (Mathematics Classes) www.pioneermathematics.com MOBILE: 9815527721, 4617721 ... 2cos x 3cosx 3 0 3 ( 3) 4(2)( 3) 3 27 cosx 2 2 4 − − = + + − − − + ± ...

    • [PDF File]Rules of Logarithms - University of Hawaiʻi

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      3. log b M log b a = M a Arrange from least to greatest: 1. e;lne;1 2 2. e2;1;lne2 3. ln 1 e;e 1;1 4. 4;ln4;e Simplify: 1. log 10 10 3 2. log 3 27 5 3 3. log 2 2 p 8 4. (ln(e2)) 1 5. 2log 2 3 log3 3 2 6.* log 2 3log 3 4log 4 8 7.* elog e3 27 Write as a sum or difference of logarithms without any exponents: 1. ln(x2 y2) 2. log 2 3x5 y8 3. log a ...

    • [PDF File]Trig. Past Papers Unit 2 Outcome 3 - PRESTWICK ACADEMY

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      Higher Mathematics PSfrag replacements O x y [SQA] 7. (a) Show that 2cos2x cos2 x = 1 3sin2 x . 2(b) Hence solve the equation 2cos2x cos2 x = 2sin x in the interval0 x < 360. 4 PSfrag replacements O x y [SQA] 8. Solve the equation sin2x +sin x = 0, 0 x < 360. 5 PSfrag replacements O x y [SQA] 9. Find, correct to one decimal place, the value of x between 180 and 270 which satises the equation ...

    • [PDF File]Answer on Question #53373 Trigonometry

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      Answer on Question #53373 – Math – Trigonometry Prove that 3sin𝑥+sin(2𝑥) 1+3cos𝑥+cos(2𝑥) =tan𝑥 where 𝑥 is a constant. Solution We’ll use next trigonometric identities

    • [PDF File]Extra Examples of Trigonometric Integrals

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      2. Z sin5 x dx = Z sin4 x sinx dx isolate one copy of sinx Z sin2 x 2 sinx dx nd remaining even powers of sinx = Z 1 cos 2x 2 sinx dx convert sin x using trig. identity u = cosx du = sinx dx du = sinx dx don’t need to expand algebra yet ...

    • [PDF File]Lesson 17: Increasing/Decreasing Functions; First Derivative Test

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      3. 1. Example 1. Find the intervals on which the functions below increase/decrease, and find the relative extrema if they exist: A. f(x) = 4x5 + 5x4 −40x3 2. B. g(x) given its derivative g′(x) = e2x(3x2 −27) 3. Example 2. The critical numbers of f(x) = 2cos(2x) + 2xon (0,2π)

    • [PDF File]POLAR CALCULUS 1. Consider the polar curve r = 1 + 2cos(2 ). x rcos and ...

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      3. Find integrals for the lengths of the two sizes of loop in r= 1+2cos(2 ). These will be (very) hard to evaluate, but you can use a calculator or computer to get approximations. 4. Find the length of the cardioid r= 1+cos . Hints: you’ll need the identity 2cos2 u= 1+cos(2u) and you’ll also need to remember that p u2 = juj.

    • [PDF File]−2π 2cos(2x)−1=0 - UNIOS

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