# d/dx ∫(2x, 0) cot(t^5)dt

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1. ### Justin wants to evaluate 3cot(-5pi/4). Which of the following identities can he use to help him? Select two answers.

cot(-theta) = cot(theta) cot(-theta) = -cot(theta) cot(-theta) = cot(-theta) cot(theta + pi) = cot(theta) cot(theta + 2pi) = cot(theta)

2. ### 1)if the graph of f(x)=cotx is transformed by a horizontal shrink of 1/4 and a horizontal shift left pi, the result is the graph of:

a) g(x)= cot[1/4(x-pi)] b) g(x)=cot[1/4(x+pi)] c) g(x)=cot[4(x-pi)] d) g(x)=cot[4(x+pi)] e) g(x)=cot[4x+pi] please include

3. ### A right triangle has acute angles C and D. If tan C=158 and cos D=1517, what are cot D and sin C?

cot D=8/15 and sin C=8/17 cot D=8/15 and sin C=15/17 cot D=15/8 and sin C=15/17 cot D=15/8 and sin C=8/17

I am not

5. ### I am having trouble with this problem.

sec^2(pi/2-x)-1= cot ^2x I got : By cofunction identity sec(90 degrees - x) = csc x secx csc-1 = cot^2x Then split sec x and csc-1 into two fractions and multiplied both numerator and denominators by csc and got: sec x

7. ### Hello,

I'm having trouble with this exercise. Can you help me? Integral of (x* (csc x)^2)dx I'm using the uv - integral v du formula. I tried with u= (csc x)^2 and used some trigonometric formulas, but the expression became too complicated, I couldn't

8. ### Use implicit differentiation to show

dy/dx = [(1-xy)cot(y)]/[x^2 cot(y) + xcsc^2(y)] if xy = ln(x cot y).

9. ### verify (csc^4-1)/cot^2x=2+cot^2x

So this is what I have so far on the left side (csc^2x+1)(cscx+1)(cscx-1)/cot^2x =(csc^2x+1)(cot^2x)/cot^2x i think I'm doing something wrong. Please help!

10. ### use the quotient and reciprocal identities to simplify the given expression

cot t sin t csc t sin t tan t cot t cot t sec t

11. ### Simplify (cos x)/(sec(x) + 1)

a. cot^2 x - cot^2 x * cos x b. cot^2 x + cot^2 x * cos x c. cos^2 x + cos x d. cot^2 x - cot^2 x * sin x

12. ### Please review and tell me if i did something wrong.

Find the following functions correct to five decimal places: a. sin 22degrees 43' b. cos 44degrees 56' c. sin 49degrees 17' d. tan 11degrees 37' e. sin 79degrees 23'30' f. cot 19degrees 0' 25'' g. tan

13. ### Verify the identity.

(csc(2x) - sin(2x))/cot(2x)=cos(2x) =csc(2x)/cot(2x) - sin(2x)/cot(2x) =csc(2x)/cot(2x) - cos(2x) Is this correct so far? If so then how would I continue? I got stuck on this part...

15. ### What is the first step. Explain please.

Which expression is equivalent to cos^2x + cot^2x + sin2^x? a) 2csc^2x b) tan^2x c) cot^2x d) csc^2x cos^2x + cot^2x + sin2^x

16. ### how do I simplify these?

1. (Cot/1-tan) + (Tan/1-Cot) - Tan - Cot 2. (1+cos) (csc-cot)

17. ### Find cot x if sin x cot x csc x = .square root 2

After reducing i got cot= square root of 2 Am i correct?

18. ### Hi everyone :)

I need a lot of help. I have many questions i don't get how to do and even if you can help me with one of them, I'd truly appreciate it. I really need the help and i gotta hand this in soon so please help if you know how to do any of these

19. ### Prove:

Cot x cot 2x - cot 2x cot 3x - cot 3x cot x = 1

21. ### Express the function in the form

f compose g. (Use non-identity functions for f and g.) u(t) = cot t/(9+cot t) {f(t), g(t)}=?

22. ### HELP!!!! I don't know how to do the trig identity with this problem

csc^4 x-cot^4x= Csx^2 x + cot^2x

23. ### prove the identity

sec^2x times cot x minus cot x = tan x

27. ### Find all angles between 0 and 2 phi inclusive which satisfy

cot 2z = 1 + cot z

28. ### sin^2 x + cos^2 x = 1

using that, derive what the cot^2 x would equal to. would it be csc^2 x - 1 = cot^2 x

29. ### If sinA=12/13 & tan B=3/4 then find

¡= sin(A+B) ¡¡=COS(A-B) ¡¡¡=COT(A-B) ¡v=cot(A-B) Sir please give me the correct ans because tomorrow is my class

31. ### Factor the trigonometric expression. There is more than one correct form of the answer.

cot^2 x + csc x − 19 NOT SURE WHETHER TO REPLACE THE COT WITH COS^2X/SIN^2X THEN CSCX TO 1/SINX?

32. ### I'm trying to verify these trigonometric identities.

1. 1 / [sec(x) * tan(x)] = csc(x) - sin(x) 2. csc(x) - sin(x) = cos(x) * cot(x) 3. 1/tan(x) + 1/cot(x) = tan(x) + cot(x) 4. csc(-x)/sec(-x) = -cot(x)

33. ### How do you simplify these equations:

1.)(2/cot^3(x) - cot^2 (x)) + (2/cot (x)-2) 2.) (2/ tan^2 (x)) + (2/ tan(x) -2)

35. ### Verify:

tan^2a=cot^2a-cot^2acsc^2a

36. ### d/dx (cot(x) / sin(x)) =

I got dy/dx= -csc(x) - cos(x)cot(x)

37. ### Verify the identity algebraically.

TAN X + COT Y/TAN X COT Y= TAN Y + COT X

38. ### Simplify the trigonometric function

sin^4⁡x-cos^4⁡x cos^2⁡â-sin^2⁡â=1+2cos⁡â (1+cot^2⁡x )(cos^2⁡x )=cot^2⁡x cot^2⁡t/csc⁡t =(1-sin^2⁡t)/sin⁡t (Work on both sides!) sinècscè- sin^2⁡è=cos^2⁡è

39. ### For each expression in column I, choose the expression from column II to complete an identity:

Column I Column II 1. -tanxcosx A. sin^2x/cos^2x 2. sec^2x-1 B. 1/sec^2x 3. sec x/cscx C. sin(-x) 4. 1+sin^2x D.csc^2x-cot^2x+sin^2x 5. cos^2 x E. tanx I figured

Simplify the expression: sin theta + cos theta * cot theta I'll use A for theta. Cot A = sin A / cos A Therefore: sin A + (cos A * sin A / cos A) = sin A + sin A = 2 sin A I hope this will

41. ### Hello

lim x->pi^- for cot(x) [In words,this is the limit of x as it approaches pi from the negative direction for the function cot(x). I am very confused as to how this occurs and turns out to be negative infinity. Thanks.]

42. ### How do we find what "a" is equal to?

I am not sure if we are supposed to put it back to tangent and then find the common denominator? Please help!?!? a cot 16 - a cot 57 = 9.167

43. ### I posted this question before at 7:14

I think the answer to it is 0. cot(40) - ((sin(50))/(sin(40)) = ? these are also degrees steps too please. I thought since 50+40= 90 then that part would be 1, but then how would cot 40 turn out to be 1

44. ### integral of cscx^(2/3)(cot^3)x

i know that cot^2x is csc^2(x)-1, but i just don't understand how to solve the cscx^(2/3), any help? i also know that its trig integrals/substitution...

45. ### Find the values of the trigonometric function cot -8/17

sin: sec: tan: cot: I know you use a Pythagorean Identity, sin^2t + cos^2t=1 I got 64/289 for the first one for example and it was wrong.

46. ### Are these correct?

5. is sin θ = -7/13 and cos θ = 12/13, find tan θ and cot θ using Quotient Identities. answers: tan (θ) = -(7/12) cot (θ) = -(12/7)

47. ### So I have a math problem where I need to solve an equation for x where x is within (0, 2pi)

I have it simplified down to cotx+cot^2x=0 and cotx-cot^2x=0 but I don't know where to go from here

48. ### Differentiate.

y= u(a cos u + b cot u) I am not sure if this correct. I was not sure whether to leave the variables as are or where the negatives should be placed? (u)*(- a sin u - b csc^2 u) + (a cos u + b cot u)*(1)

56. ### I don't think its right . can you correct me please .

A.log sin A = 9.91655 - 10 sinA = 0.82537 A = 55.626° = 55° 34' 35" B.log cot A = 0.11975 cot(A) = 1.317498... A = 37.199 degs A = 37º 11' 56"

57. ### I don't think its right . can you correct me please .

A.log sin A = 9.91655 - 10 sinA = 0.82537 A = 55.626° = 55° 34' 35" B.log cot A = 0.11975 cot(A) = 1.317498... A = 37.199 degs A = 37º 11' 56"

58. ### Cot 495 degrees... a) -tan 135 degrees

b) -cot 135 degrees c) cot 135 degrees d) -cot 315 degrees

59. ### Hello all,

In our math class, we are practicing the trigonometric identities (i.e., sin^2(x)+cos^2(x)=1 or cot(x)=cos(x)/sin(x). Now, we are working on proofs that two sides of an equation are equal (for example, sin(x)*csc(x)=1;

60. ### how do you veriy

tan x + Cot y -------------- = tan y + cot x 1-tan x cot y sin^4x + cos^4x = 1- 2cos^2x + 2cos^4

61. ### How would I evaluate these trig functions without using a calculator? U:

sin(-13π/6) cot 11π/6 cot(-14π/4) sec 23π/6 Thanks in advance ^^; and if you'd tell me step by step on how to do problems like these I'd be grateful :D

62. ### Without using tables, evaluate:

(4 tan 60° sec 30° ) + [(sin 31 sec 59° + cot 59° cot 31°)/ (8 sin² 30°-tan² 45°)]

63. ### Prove the following identity:-

(i) tan^3x/1+tan^2x + cot^3x/1+cot^2 = 1-2sin^x cos^x/sinx cosx

65. ### Simplify the follow)ing to the simplest form

(tan(x) +cot(x))/ (tan(x)*cot(x))

66. ### Find the derivative of

y=cot³(1-2x)² y'=3[cot(1-2x)²]² (-csc²(1-2x)²)(2-4x)(-2) y'=(-6+24x)[cot(1-2x)²]²(-csc²(1-2x)²) How do you simplify further?

67. ### If A+B+C=180 and sin a= sin b sin c prove that

cot a= 1- cot b cot c

68. ### Julia wants to simplify the term sec^2 theta-1/cot^2 theta+1 in a trigonometric identity that she is proving. Which of the following identities should use to help her? Select all that apply. (2 ANSWERS)

a. sin^2 theta+cos^2 theta=1 b. sec^2 theta-tan^2

69. ### Solve and prove the identity

(tan x+ cot (-x))/ (tan x - cot(-x))= 1-2cos^2(x)

70. ### Use the given information to evaluate cos (a-b).

Cot a = 3/4, cot b = 24/25; pi<a<3pi/2, 3pi/2<b<2pi.

71. ### Find the values of the six trigonometric functions of θ. (If an answer is undefined, enter UNDEFINED.)

Function Value: csc(θ) = 4 Constraint: cot(θ) < 0 1) sin(θ)= 2) cos(θ)= 3) tan(θ)= 4) csc(θ)= 5) sec(θ)= 6) cot(θ)=

72. ### Prove:

sin^2(x/2) = csc^2x - cot^2x / 2csc^2(x) + 2csc(x)cot(x) On the right, factor the numberator as a difference of two perfect squares. In the denominator, factor out 2cscx. You ought to prodeed rather quickly to the proof.

73. ### For all values x for which the terms are defined, fidnteh value(s) of k, 0<k<1, such that

cot(x/4) - cot(x) = [sin(kx)]/[sin(x/4)sin(x)] PLEASEEEE HELP! ASAP!

74. ### Determine the values of sin, cos, tan, csc, sec and cot at (-3, -3) on the terminal arm of an angle in standard position

2. If cos θ = 2/3 and 270° < θ < 360° then determine the exact value of 1/cot

75. ### Find the complete solution of each equation. Express your answer in degrees.

sec^2 θ+sec θ=0 2 cos^2 θ+1=0 cot θ=cot^2 θ sin^2 θ+5 sin θ=0

76. ### Find the complete solution of each equation. Express your answer in degrees.

sec^2 θ+sec θ=0 2 cos^2 θ+1=0 cot θ=cot^2 θ sin^2 θ+5 sin θ=0

77. ### Two questions that I would really appreciate some hints on:

1) Circles with centers (2,1) and (8,9) have radii 1 and 9, respectively. The equation for a common external tangent can be written in the form y=mx+b with 0<m. What is b? 2) In triangle ABC,

79. ### Which of the following expressions have a value of −3–√?

sin(11π/6) cos(5π/3) cot(7π/6) tan(11π/6) cot(2π/3) sin(5π/3) csc(5π/3) cos(7π/6) cos(π/6) csc(2π/3) I think none..but that is not an option...so do I go with cot(7π/6) thanks

80. ### Which of the following expressions have a value of –√3?

sin(11π/6) cos(5π/3) cot(7π/6) tan(11π/6) cot(2π/3) sin(5π/3) csc(5π/3) cos(7π/6) cos(π/6) csc(2π/3) I think none..but that is not an option...so do I go with cot(7π/6) thanks

81. ### Can someone help me find the exact value of 4csc(3pi/4)-cot(-pi/4)?

Thanks! cotx =1/tanx cscx = 1/sinx If you find it easier to conceptualize in degrees, realize that pi/4 radians is 45º and 3pi/4 is then 135º If you know the CAST rule, it is easy to see

7. What is 1/cot(x) in terms of sine? This is what I've got so far: sin = 1/csc tan = 1/cot 1+cot2(x) = csc2(x) 1/1+cot2(x) = 1/csc2(x)

83. ### Please show how to do these problems so i understand.

1)Prove that sin^2 x (1+cot^2 x)=1 2)Prove that tan x (cot x+tan x)=sec^2 x

84. ### Please show how to do these problems so i understand.

1)Prove that sin^2 x (1+cot^2 x)=1 2)Prove that tan x (cot x+tan x)=sec^2 x

85. ### could someone please tell me what the other angle identity of tan is? Thank you much!

"...other angle identity of tan x"? in relation to which "other" ? there are many identities dealing with the tangent. The most important is probably tan x = sin x/cos x

89. ### 1)Find cos theta if sin theta=3/5 and 90 degrees<theta<180 degrees.

A)4/5 B)-4/5 C)square root of 34/5 D)-square root of 34/5 I chose A 2)Simplify:1-csc^2theta/cot^2theta A)-1 B)1 C)tan^2theta D)1/sin^4theta I chose C 3)Simplify:-5(cot^2theta-csc^2theta)

90. ### Verify the following:

1. cos x/(1-sinx)= sec x + tan x 2. (tanx+1)^2=sec^2x + 2tan x 3. csc x = )cot x + tan x)/sec x 4. sin2x - cot x = -cotxcos2x

91. ### Let f(x)=cot(x). Determine the points on the graph of f for 0<x<2π where the tangent line(s) is (are) parallel to the line y=−2x.

so i've derived f(x) = cot(x) and have gotten f'(x)=-csc^2(x) which then I've made f'(x)=-2x so now i have -2x=-csc^2(x) or

92. ### Which expression is equivalent to tan theta-sec theta/sin theta?

A)-cot theta B)cot theta C)tan theta-cot theta D)tan theta-sec^2theta just tell me what I need to know to set it up

93. ### sec theta 5 need to find

cos theta cot theta cot (90-theta) sin theta not sure what to do completely confused on this stuff

94. ### We're doing indefinite integrals using the substitution rule right now in class.

The problem: (integral of) (e^6x)csc(e^6x)cot(e^6x)dx I am calling 'u' my substitution variable. I feel like I've tried every possible substitution, but I still haven't found

95. ### Find an equation for the tangent line to the curve at (π/2 , 2).

y = 4 + cot(x) - 2csc(x) I am confused how to take the derivative of this problem. When I tried to solve it I ended up with -csc^2 (x) + (2csc(x) * cot(x)). From there I can't seem to

96. ### Q.1 Prove the following identities:-

(i) tan^3x/1+tan^2x + cot^3x/1+cot^2 = 1-2sin^x cos^x/sinx cosx (ii) (1+cotx+tanx)(sinx-cosx)/sec^3x-cosec^3x = sin^2xcos^2x.

97. ### Q.1 Prove the following identities:-

(i) tan^3x/1+tan^2x + cot^3x/1+cot^2 = 1-2sin^x cos^x/sinx cosx (ii) (1+cotx+tanx)(sinx-cosx)/sec^3x-cosec^3x = sin^2xcos^2x.

98. ### Which of the following are trigonometric identities? Select all that apply (there are 3 answers).

A cos^2(theta)=sin^2(theta)-1 B sin(theta)=1/csc(theta) C sec(theta)=1/cot(theta) D cot(theta)=cos/sin(theta) E 1+cot^2(theta)=csc^2(theta)

99. ### Use the fundamental identities to simplify the expression:

cot beta sec beta I used 1+tan^2u=secu since cot is the inverse of tan. I flipped the tangent, then so it was 1+ (1/tan). But the book's answer is the cosecant of beta. Where did this come from??

100. ### sorry, another I can't figure out

Show that (1-cot^2x)/(tan^2x-1)=cot^2x I started by factoring both as difference of squares. Would I be better served by writing in terms of sine and cosine? Such as: [1-(cos^2x/sin^2x)]/[(sin^2x/cos^2x)-1]=(cos^2x/sin^2x)