5. Determine the exact value of sin 1l7 |. Include a clearly labelled diagram. [3 marks]

Q: Give the degree of 0 = tan-(-V3) if it exists. measure %3D

A: topic - inverse trigonometric ratios

Q: tan x[cot x – cos x]dx

A: Here we can find the integration as below

Q: 18. Use periodicity to express sec in p given that sin

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Q: Find Taylor's Sen'ed fey ci) f(x) = sin (2) about x= 1

A: see 2nd step.

Q: b. Prove that 2cot (20) = cot(0) - tan(0)

A: To prove the identity.

Q: Q3) Ify = in[sec 8 + tan 8) find

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Q: Prove the following inequalities (ii) -10|< sin 0 < |0| and -|0| < 1– cos 0 < |0|

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Q: Find sin 2x, cos 2x, and tan 2x if tanx= and x terminates in guadrant III. 3

A: To find the value of sin (2 x), cos (2 x), and tan (2 x).

Q: is: The number of zeros of sin(-) is: `z-1

A: If y=f(z), then the variable z is called the input of the function, and y is called the output of…

Q: 1. Differentiate the following with respect to the variable given. 1 cosx 2 sin' x tan

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Q: Find an expression that is mathematically equivalent to (1 - cos(x) / 2) and in which excessive…

A: We will find the expression mathematically equivalent to the given term as following.

Q: 6. By using u = tan 0, evaluate | tan 0 sec*e de .

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Q: find @ Sin 2TTH Sin 4TTH lt 2. 0.7073in21t icdt

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Q: 2. Extend the identity cos(ax)-cos?x-sin'x for xE PR to the identity cas (a2)- Cos s 2-sinz for & €…

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Q: 4) state laylors your estima te 5) Using in Taylor's Theorem, show that the error in 3) for cos…

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Q: 2 _ 2 if tane + sin0= m and tan0 – sin0 = n ,show that m² – n´ = 4 mn

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Q: Find sin(2x), cos(2x),and tan(2x) from given information. sex(x)=6 , x in Quadrant IV • sin(2x) =…

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Q: 1) Find thesexact value o niSinG/2) ban sin x Ei Joven that 4 2.

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Q: Use De Moivre's Theorem with n= 3 to express cos 3θ and sin 3θ in terms of cos θ and sin θ.

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Q: 5. Estimate to 4th place accuracy, i.e. within 0.00005 of cos(2º) using its Mac- xpansion. Justify…

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Q: 4. Use the inequality | sin r|< |x| for x E R to show that the sine function is continuous at r = 0.…

A: Sine function and it's continuity at 0

Q: 40 a) Find sin' xcos' xdx by using substitution u = cosx.

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Q: 3. Give upper and lower estimates (in terms of n alone) for sin nb COs na + valid for all a, b; show…

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Q: For what values of x in [0, 27] does the graph of f(x) = x + 2 sin æ have a horizontal tangent line?…

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Q: 14. Evaluate cos 3x+ dx. 2

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Q: Compute | a° sin(æ" + 2) dæ.

A: Given : ∫x6sinx7+2dx

Q: Draw the following graph on the interval– 315° < < 60°: - y = - 3 cos(r - 90°) %3D

A: Given,           The function is y=-3cosx-90° on the interval -315°&lt;x&lt;60°.

Q: 35. Use property IV of Appendix A to verify that 1 L'{arctan(a/s)} =sin at

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Q: 6. Suppose that < 0 < n and sin 0 = . Find the other 5 trigonometric functions evaluated at 0.

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Q: Use De Moivre’s Theorem with n = 3 to express cos 3θ and sin 3θ in terms of cos θ and sinθ.

A: To express cos3θ and sin 3θ in terms of cosθ and sinθ, using De Moivre's theorem with n=3. De…

Q: Make a table using multiples of x/4 for x to sketch the graph of y = cos 2x from x = 0 to x = 2x. y…

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Q: 2. Suppose tan x = 3 -- with < x < 2n. Find the exact value of cos ). Show you work carefully. ensem…

A: Given problem:- tan(x) =-4/3 with 3π/2 &lt;x&lt; π To find:- Exact value of cosx2)

Q: Evaluate the integral: 3 X sin ³ COS 3 3 X col 3

A: Solved below.

Q: (b) Can we use the IVT to conclude that f (x) = tan(x) equals 0 for some c in (0, 1)? %3D

A: We can answer first question among which you asked as per the honor policy. please resubmit the…

Q: 4 Find sin 2x, cos 2x, and tan 2x if cosx= and x terminates in guadrant III.

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Q: 10. Evaluate cos x sin² x dx

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Q: Use Simpson's rule with n = 4 to approximate /" cos(2) -dr

A: Given: ∫16cosxxdx Here a=1, b=6 and n=4  h=b-an∆x=6-14∆x=54∆x=54

Q: 15. Evaluate | sin° x cos xdx 3

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Q: 6. Use the Intermediate Value Theorem to show that the following equation has at least TWO distinct…

A: Intermediate Value Theorem states that ''If a continuous function has values of opposite sign inside…

Q: 5. Integrate the following and show all of your work: sin“ r cos r dr

A: we have to integrate the following

Q: Find sin 2x, cos 2x, and tan 2x if tanx=-. and x terminates in guadrant IV 3

A: sin 2x= 2 sin x cos x cos 2x=1-2sin2x tan 2x=(sin 2x)/(cos 2x)

Q: Show that : |sin x |= CoS nX Σ n2 even 414 2/7

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Q: (6) Given that In= tan" x dx, show that, for n 2 2. %3D In- In-2 = %3D n- 1

A: I think given question is slightly wrong. According to me the required proof should be…

Q: 33. Use addition formulas and the values of sin 0 and cos 0 for 0 = to compute sin 12 and cos…

A: Given: sin7π12, cos7π12 We know that sinA+B=sinAcosB+cosAsinB…

Q: 5.3 Evaluate (sin (x)cos“(x)dx

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: Assume sin(0) = 12 where 0 < 0 <. Compute the following in terms of x. tan (20) cos (2) - -

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Q: Show that 1 − cos x = x2/2 with an error less than 0.003 for |x| &lt; 1/2.

A: Given: 1-cos x =x22;    |error|&lt;0.003Formula:  The…