Sec x 2 2 tan x

    • [PDF File]Grosse Pointe Public School System / GPPS Home

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      tan x = cosx = — and tan 2x using the given information. 30 sec x = 2; sin x < 0 29 2SthktOSL Cos2x.: x in Q2 sin 2x = cos2x = tan 2x = — 1-(-5E IS sin 2x = cos 2x = -25 tan 2x = sin— = 10 cos— = 10 31. Find tan 2x if cscx = 4 and tan x < 0. In #32 & 33, find sin£ and cosE using the given information. 10 to 32. 1800 < x < 2700

    • [PDF File]Trigonometric Identities Worksheet

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      Trigonometric Identities Worksheet . I. Prove each identity . 1) tanxcos x = sinx . 2) cotxsec x = esc . x 3) sin . x . cot . x == cos . x 4) tan . xcsc x . sec

    • [PDF File]Math 2260 Exam #2 Practice Problem Solutions

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      The left hand side is easy; for the right hand side, let x= tan . Then dx= sec2 d , so Z dx x 2+ 1 = Z sec2 d tan + 1 = Z sec2 d sec2 = + C: 3. Therefore, since = arctan(x), we see that the above equation between integrals is equivalent to lny= arctan(x) + C: Exponentiating both sides, we have that

    • [PDF File]TRIGONOMETRY LAWS AND IDENTITIES

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      TRIGONOMETRY LAWS AND IDENTITIES DEFINITIONS sin(x)= Opposite Hypotenuse cos(x)= Adjacent Hypotenuse tan(x)= Opposite Adjacent csc(x)= Hypotenuse Opposite sec(x)= Hypotenuse Adjacent

    • [PDF File]1 Integration By Substitution (Change of Variables)

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      Solution6. We rst do a trick by multiplying the numerator and denominator by sec(x) + tan(x), Z sec(x)dx= Z sec(x)(sec(x) + tan(x)) sec(x) + tan(x) dx= Z sec2(x) + sec(x)tan(x) sec(x) + tan(x) dx: Step 1: We will use the change of variables u= sec(x) + tan(x), du dx = sec(x)tan(x) + sec2(x) )du= (sec(x)tan(x) + sec2(x))dx: Step 2: We can now ...

    • [PDF File]Trig Substitution

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      (sec tan )(sec2 1)d Now, we use u-substitution with u= sec , du= sec tan d : 1000 Z (sec tan )(sec2 1)d = 1000 Z (u2 1)du = 1000 1 3 u3 + u + C: P4.The integral found above is in terms of uwhile the the original question was in terms of x. This means we need to back-substitute. The rst substitution is easy: Because u= sec ,

    • [PDF File]Limits using L’Hopital’s Rule (Sect. 7.5) 0 L’Hˆopital’s ...

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      sec(x) tan(x) = 1 cos(x) cos(x) sin(x) = 1 sin(x) ⇒ L = 1. C We now try to compute this limit using L’Hˆopital’s rule. Indeterminate limit ∞ ∞ Example Evaluate L = lim x→(π 2)− sec(x) tan(x). Solution: This is an indeterminate limit ∞ ∞. L’Hopital’s rule implies L = lim x→(π 2)− (sec(x))0 (tan(x))0 = lim x→(π 2 ...

    • [PDF File]File Revision Date : CHAPTER 8 visit www.cbse.online or ...

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      ^^sec tan sec tanBBCCx--hh= then the value/ values of x is/are (a) !1 (b) 0 (c) !2 (d) 1 Ans : (a) !1 We have, ^^^sec tan sec tan sec tanAABBCC++ +hh h =^hsec tanAA-^^sec tan sec tanBBCC--hh On multiplying both sides by ^^^sec tan sec tan sec tanAABBCC-- -hh h, we get ^^^sec tan sec tan sec tanAABBCC++ +hh h # ^^^sec tan sec tan sec tanAABBCC ...

    • [PDF File]4. THE FUNDAMENTAL TRIGONOMETRIC IDENTITIES trigonometric ...

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      csc sec csc sec 2 2 2 x x x + x 33. csc ( tan cot ) sec α α α α + 34. γ γ γ 1 sec sin tan + + 35. θ θ sec 1+tan 36. 1 - tan ( ) cot ( ) 1 t t − − − 37. u u u u cot csc tan sin + + 38. β β β β β β − tan + + csc csc csc tan csc In problems 39 to 44, rewrite each expression in terms of the indicated function only. 39.

    • [PDF File]Trigonometric Identities

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      1−cos2 x cosx =1−cos2 x =sin2 x Example 3 Express 1− 1 cscx 2 +cos2 xin terms of sin 1− 1 cscx 2 +cos 2x =(1−sinx) +cos2 x =1−2sinx+sin2 x+cos2 x =2−2sinx 2 Other Identities 2.1 Sum and Difference Identities 2.1.1 The Identities Proposition 4 Let α and β be two real numbers (or two angles). Then we have: 1. sin(α+β ...

    • [PDF File]Lecture 6 - University of Houston

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      Lecture 6 Section 7.7 Inverse Trigonometric Functions Section 7.8 Hyperbolic Sine and Cosine Jiwen He 1 Inverse Trig Functions 1.1 Inverse Sine Inverse Since sin−1 x (or arcsinx) 1

    • [PDF File]A BRIEF GUIDE TO CALCULUS II - University of Minnesota

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      sin2 x +cos2 x = 1 sec2 x = tan2 +1 csc2 x = cot2 +1 Half Angle Formulas sin2 x = 1 2 (1 cos2q) cos2 x = 1 2 (1 +cos2q) Double Angle Formula sin2x = 2sin x cos x These identities are far a from complete, but they will suffice for most of the problem that we will encounter. To illustrate this, we will present the common strategies for ...

    • [PDF File]Trigonometric Integrals

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      cos(x), sin(x), tan(x), sec(x), csc(x), cot(x). The general idea is to use trigonometric identities to transform seemingly difficult integrals into ones that are more manageable - often the integral you take will involve some sort of u -substitution to evaluate.

    • [PDF File]C3 Trigonometry - Trigonometric identities

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      (b) y = sec x, −. 3 π ≤ x ≤. 3 π, stating the coordinates of the end points of your curves in each case. (4) Use the trapezium rule with five equally spaced ordinates to estimate the area of the region bounded by the curve with equation y = sec x, the x-axis and the lines x = 3 π and x = −. 3 π, giving your answer to two decimal ...

    • [PDF File]Trig Cheat Sheet - Lamar University

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      x q==x 1 sec x q= tan y x q= cot x y q= Facts and Properties Domain The domain is all the values of q that can be plugged into the function. sinq, q can be any angle cosq, q can be any angle tanq, 1,0,1,2, 2 qpnn

    • [PDF File]Antiderivative of tan x sec2x - MIT OpenCourseWare

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      Figure 1: Graphs of 2tan2 x (blue) and sec x (red). In fact, that is the case: sin2 x tan2 x = cos2 x 1 2− cos x = cos2 x = sec 2 x − 1 1 2 1 2 1 We conclude that tan x = sec and so the two results are equiva­

    • [PDF File]Tangent, Cotangent, Secant, and Cosecant

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      The range of cscx is the same as that of secx, for the same reasons (except that now we are dealing with the multiplicative inverse of sine of x, not cosine of x).Therefore the range of cscx is cscx ‚ 1 or cscx • ¡1: The period of cscx is the same as that of sinx, which is 2….Since sinx is an odd function, cscx is also an odd function. Finally, at all of the points where cscx is ...

    • [PDF File]Edexcel - Kumarmaths

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      (a) Use the substitution t = tan x to show that the equation 4tan 2x – 3cot x sec2 x = 0 can be written in the form 3t 4 + 8t 2 – 3 = 0 (4) (b) Hence solve, for 0 ≤ x < 2𝜋, 4tan 2x – 3cot x sec2 x = 0 Give each answer in terms of 𝜋. You must make your method clear. (4) [2015, June, IAL Q7] 31. (a) Show that cot2x – cosec x ...

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