D let cOs x ) and cos x lies below the x axis e Find sin(2x), cos(2x) and tan (ex). ) Proof the Lormula of unit circle X+y=1,and exPlain it in your A OWn Words.

Q: 13. Given y = arcsin(x) – x/1-x² , what is y'? 2r? A) |1-. 2x B) C) D)

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Q: Let P(t) = (x,y) be the terminal point on the unit circle that corresponds to the real number t.…

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Q: Determine the concavity and find the poir (a) y = 2 cos x + sin 2x, 0 < x < 2T %3D

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Q: -V5 & cos B<0. 8) cot given tan B = %3D

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Q: dy - cosec'x. cos x (i) By differentiating 6 show that if y = cot x then sinx' dr (ii) Show that x…

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Q: 35. The cissoids r = a sin 0 tan 0. (See Exercise 29.) Ans. sin 0 cos 0 dr - r(1+ cos? 0) d0 = 0.

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Q: Eliminate 0 from the equations : (i) x = h + a cos 0, y = k + b sin 0 (ii) x = a ser³ 0, y = b cot³…

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Q: (a) Find a function u(x, y) that is harmonic in R2 and that equals f(8) sin(30) + cos(40) on the…

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Q: The region inside both of the circle r = 2 sin 0 and r =1. Which of the following gives the area of…

A: Let us consider the double integartion ∫R∫f(r,θ) drdθ where R is the region of integartion in the…

Q: f Px) and Pn) are points in quadrant Il on the terminal side of the angles x, and xy, respectively,…

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Q: How can we find x using SohCahToa? sin 34 = %3D y cos 34 = tan 34 = 34°

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Q: a. Y = cot(Ve“ ) tanh(e") -1 (sin(x²)) tan(2²) tan(ray) = x + y? b. y = C.

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Q: 1- cos A + sin A -then 2 sin A If y = is equal to 1+ cos A + sin A 1+ sin A

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Q: HW: (1) Prove that : cos e (a) sin e =1, (b) tan? 0.cos0+ cot? 0.sin?0=1 %D 1-tan 6 1- cot' 8 (h)…

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Q: TC + (c) Given that In = tan" x dx , show that %3D In + In-2 = (n 2 2) %3D Hence, find 8. tan (2x)…

A: Given an integral : In=∫0π/4tannx dx We need to show : In+In-2=1n-1 , n≥2 Also we need to find…

Q: B)Prove (cose + i sine)" = cosno + i sin no

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Q: 2. If P(x, y) is on the unit circle, then x? + y? = So for all i we have sin't + cost =

A: We Know that, In case of the unit circle: Radius r = 1 and  Standard form of circle passes through…

Q: 2) Given y = Cos x and y= 20 Period 28 D Period = X Degrees y= Cosx 1

A: Given  y=cosx and y=2cosπx the period of a cos function is 2π so period=2π/b =2π which implies that…

Q: 6. Find centre and radius of the circle (x- a )? + y? = c² %3D वृत्त (x -a)+ ५2%3D c2 के केन्द्र एवं…

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Q: 3- + y cot x = 2 cos x %3D dx

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Q: If sin t = 3 and t is in the 2"d quadrant, then i) tant = ii) sec t =

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Q: The arc length of the graph of y = In(cos æ) from the point where a = 0 to the point where a I is…

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Q: 27. The perpendicular distance ON from the origin t line L is p, and ON makes an angle a with the…

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Q: 3. Using the fact that sin 2a = 2 sin a cos a, and the fact that 0 = 2a, rewrite the area of the…

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Q: (g Suppose cos(a) = - and sin(a) is positive. 3 If the point (-2, y) is on the terminal side of the…

A: Given,           cosα=-23 and sinα is positive. Also, the point -2,y is on the terminal side of the…

Q: 12. Explain why using trigonometric substitution with x = a tan u often involves a triangle with…

A: Consider the right triangle below with angle u , opposite side x and adjacent side a.

Q: Assume that a particle’s position on the x-axis is given byx = 3 cos t + 4 sin t,where x is measured…

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Q: How many petals does the rose curve r = 3 sin 40 have in the interval [0, T]? O 16 O 4 O 8

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Q: Match the ratios for sin X, cos X and tan X. X Y sin X DRAG & DROP THE ANSWER cos X 7 tan X 4/2 4/2…

A: Use the defination of  trigonometric ratios and find value of each trigonometric ratios.

Q: tan z cos a 1 -dr = cos? z O a. sin a - sec" r +C O b. cos? z 1+ C O C. sec a tan a + C O d. – tan a…

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Q: Trace the curve: r = 1/2 sinꝋcos^3ꝋ.

A: The equation of the curve is r=12sin θcos3θ. First check the the symmetry of the curve. The curve is…

Q: The curves r1(t) (5t, t,- 2t') and 72(t) = (sin(- 4t), sin( – 3t), t - T) intersect at the origin.…

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Q: Using the identity, sinh y cosh y + i cos? x + sinh? y sin x cos x tan(x + iy) : cos² x + sinh² Y…

A: Given that, tanx+iy=sinxcoscos2x+sinh2y+isinhycoshycos2x+sinh2y Now,…

Q: sin" e de, (b) Given that In %3D Show that forn 2 2, n- In-2 %3D Hence, evaluate I5.

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Q: Sketches of y=sinx,y=cos× and y=tanx on separate sets of axes if xe(0°;360°)

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Q: cot a In(sin r) dr "/2

A: We know that integration of xn is xn+1/n+1. We know that : cosx/sinx= cotx.   Here i attached…

Q: tinuous, prove that T/2 T/2 f(cos x) dx = f(sin x) dx (b) Use part (a) to evaluate /2 cos?x dx and…

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Q: find dp/ dq. sin q + cos q = cos q

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Q: ind the area inside the circle r = cos 0, but outside the circle r =| = 1/2. Sketch the graphs…

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Q: f tan(0): and sin(0) < 0, then 3 %3D sin(e) = %3D cos(0) = %3D sec(0) = csc(0) = cot(0) =

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Q: PPE Solu by hand 36(Cos 35+ J sin 30) 3((os 50°+ Jsin soo) Trignometric i

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Q: s).F ecosa sin a da cos a sin a da 2

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Q: When using u substation what should I use as the u when the problem is the intergral of…

A: Explanation:The given integral is ∫cos3(θ)sin(θ)dθ.

Q: 7 - If æy + sin(e") + arcsin a = sin 1+ then what is the value of at (4, 0)? b) а) b) b. c) C d) d.…

A: Given: xy+siney2+sin-1x=sin1+π6

Q: 28. Inside the circle r = –2 cos 0 and outside the circle r = 1

A: Kindly go through the solution and let me know in case of any doubt or further clarification in the…

Q: | b, sin nx cos mx dx — п

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Q: 3. Determine the corresponding reciprocal ratio that corresponds to cos e= 0.8. а. sec e= с. sec e=…

A: 3) Given: cosθ=0.8 To find: The corresponding reciprocal ratio that corresponds to cosθ=0.8.

Q: a) Use the formulas  sin(A + B) and sin(A - B) for toshow that sin A cos B = 1/2 [sin(A - B)+ sin(A…

A: a) Use the formulas  sin(A + B) and sin(A - B) for toshow that sin A cos B = 1/2 [sin(A - B)+ sin(A…

Fundamentals of Trigonometric Identities

Trigonometric Identities are the equalities that involve trigonometry functions and hold for all the values of variables given in the equation.