Cos x 4 csc x

• [PDF File]CHAPTER 5 Analytic Trigonometry

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  Section 5.1 Using Fundamental Identities 381 9. is in Quadrant II. csc x 1 sin x 3 2 sec x 1 cos x 3 5 5 cot x 1 tan x 5 2 cos xtan 1 sin2 x 1 4 9 5 3 sin x 2 3, tan x 2 5 5 1 ⇒ x sin x sin x 2 3 ⇒ sin x 2

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• [PDF File]Trig Cheat Sheet - Lamar University

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  csc y q= cos 1 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

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• [PDF File]Equivalent Trigonometric Expressions

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  CSC x undefined and when csc(x) is zero or undefined Non-permissible values may be more easily identified from the non-simplified equivalent expression 1 + cot(x) CSC x sin(z) We see that sin(x) 0 so x n7r,n e Z Note that csc(x), that is will never equal zero. sm 1 + cot(x) = sin(x) + cos(x) for all real values of x, x nar, n e Z. Therefore csc(x

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• [PDF File]18 Verifying Trigonometric Identities

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  (x 2)(x+ 2) = x2 4 or x2 1 x 1 = x+ 1 are referred to as identities. An identity is an equation that is true for all values of xfor which the expressions in the equation are de ned. For example, the equation (x 2)(x+ 2) = x2 4 is de ned for all real numbers x. The equation x2 1 x 1 = x+ 1 is true for all real numbers x6= 1 :

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• [PDF File]Trigonometric Identities

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  g) cos(x+y) h) cos(x y) i) tan(x y) j) tan(x y) k) csc(x y) l) cot(x+y) 4. If x is an angle in the –rst quadrant with sinx = 4 5, and y is an angle in the fourth quadrant with cosy = 2 3, determine the exact value of each expression: a. sin(x y) b. cos(x+y) c. sin(x+y) d. tan(x y) e. sec(x y) f. cot(x+y) The Double Angle Formulas

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• [PDF File]CHAPTER 5 Analytic Trigonometry

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  Section 5.1 Using Fundamental Identities 439 1. csc x 1 sin x 1 3 2 2 3 2 3 3 sec x 1 cos x 1 21 32 2 cot x 1 tan x 1 3 3 3 tan x sin x cos x 3 2 1 2 3 sin x 3 2, cos x 1 2 ⇒ x is in Quadrant II. 3. is in Quadrant IV. csc 1 sin 2

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• [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

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• [PDF File]Trigonometric Identities and Equations

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  4. If csc a, then . 5. If sec 1, then cos 1. 6. If cot 1, then tan 1. Ratio Identities Unlike the reciprocal identities, the ratio identi-ties do not have any common equivalent forms. Here is how we derive the ratio identity for tan : sin cos y r x r y x tan sin 1 a cot 1 2 sec 2 √3 cos √3 2 csc 1 sin 1 3 5 5 3 csc 5 3 sin 3 5 Examples 1 ...

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• [PDF File]Basic Trigonometric Identities

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  BCCC ASC Rev. 6/2019 Basic Trigonometric Identities Reciprocals sin(𝑥)= 1 csc(𝑥) ( csc𝑥)= 1 sin(𝑥) cos(𝑥)= 1 sec(𝑥) sec(𝑥)= 1 cos(𝑥)

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• [PDF File]State College Area School District / State College Area ...

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  CSC D. secx tan x cot x cscx Sl'n x esc Y Verify each identity. Remember to work on one side independently of the other. 3. sinxsecx= tan x Ian x *any = X 5. cosxcscx = cot x cosy • COS 4. cotxcscxcosx= I . (osx 6. cot(—x)sinx=— cos x -co+ sinx Practice page I 8. cos —— x sec cscx cosxtanx = 1 Sin L cscL

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

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  24 y x O θ - θ P = ( x, y) = (cos θ, sinθ) Q = ( x, –y) = (cos(− θ), sin(−θ))unit circle Figure 4.1 4. THE FUNDAMENTAL TRIGONOMETRIC IDENTITIES A trigonometric equation is, by definition, an equation that involves at least one trigonometric function of a variable. Such an equation is called a trigonometric identity if it is true for all values of the variable for which both sides ...

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• [PDF File]Trigonometry - Andrews

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  4-04 Right Triangle Trigonometry and Identities ›Basic Identities ›Reciprocal ›sin = 1 csc cos = 1 sec tan = 1 cot ›csc = 1 sin sec = 1 cos cot = 1 tan ›Quotient ›tan =sin cos cot =cos sin ›Pythagorean ›sin2 +cos2 =1 1+tan2 =sec2 cot2 + 1=csc2 ›Note: sin2 = sin 2 26

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• [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 ...

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• [PDF File]Advanced Algebra w/Trig Name

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  x x xcos sec cos 2. 2 2 1 sec cot x x 3. 22 11 sec cscTT 4. sin 1 csc T T Verify each Identity. 5. 2 22 2 sin 1 tan sec cos x xx x 6. 2 2 1 1 cot 1 cos x x 7. 1 cot sin cos 1 cot sin cos x x x x x x 2 8. sec 1 cos tan sin x xx x

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• [PDF File]Trigonometry Lecture NotesChp6

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  Perhaps this strategy will enable us to transform the left side into csc x, the expression on the right. sec xcot x = 1 cos x • cos x sin x = 1 sin x = csc x Example 43 Verify the identity: sin tan cos secx x x x+ = Example 44 Using Factoring to Verify an Identity Verify the identity: cosx - cosxsin 2x = cos 3x

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• [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 ...

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• [PDF File]Cosecant, Secant, and Cotangent

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  csc( + 2ˇ) = 1 sin( + 2ˇ) = 1 sin( ) = csc( ) Similarly, the secant function has the same period, 2ˇ, as the function used to de ne it, cosine. Even and odd Recall that an even function is a function f(x) with the property that f( x) = f(x). Examples include x2, x4, x6, and cosine. We can add secant to the list of functions that we know are ...

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• [PDF File]5-1 Study Guide and Intervention - MRS. FRUGE

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  sin x + cos x cot x 3. csc 2 𝑥 1 + tan2 𝑥 4. (sec x – tan x)(csc x + 1) 5. (cot2 2x + 1)(sec x – 1) 6. 1 + tan 2 𝑥 1 + sec 𝑥 7. csc x sin x + cot2 x 8. cos x (1 + tan2 x ) 9. cos (π 2 – 𝑥) csc 𝑥 x 𝐢 10. cos (π 2 – 𝑥) csc 𝑥 + cos2 x csc xcsc 𝐜 xcot 𝐞𝐜 xsec 𝐜 𝐜 xsec 1

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• [PDF File]DIFFERENTIATION RULES

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  Remember, they are valid only when x is measured in radians. 22 (sin ) cos (csc ) csc cot (cos ) sin (sec ) sec tan (tan ) sec (cot ) csc dd x x x x x dx dx dd x x x x x dx dx dd x x x x dx dx DERIVS. OF TRIG. FUNCTIONS. ... s = f(t) = 4 cos t Find the velocity and acceleration at time t and use them to analyze the motion of the object.

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