i 74. Trigonometric Substitution Use the trigonometric substitution u = a tan 0, where – n/2 < 0 < n/2 and a > 0, to simplify the expression Ja² + u².

Q: A trigonometric function is graphed below. y 21 3/2 -T12 3n2 21 -11 Which function could this graph…

A: Find the trigonometric function for the given graph

Q: 4 Using trigonometric substitutions, ſ xV16 dx is equal to: - x V16 – x2 + C /16 - x2 -In -4ln + C…

A:

Q: 4. (a) (i) Without using a calculator, evaluate /2 sin 2.r cos x dx. (ii) Use the definitions of…

A:

Q: 3. Consider sin(x) cos(x) d.r. Evaluate it first by substituting u1 = sin(x), then again by…

A:

Q: 2 a) FACTOR : sec´x + 3tan x + 1 b) PERFORM THE ADDITION(SIMPLIFY) 1. 1 1 t Sine 1-sin e

A:

Q: 4x? )(i) Use the substitution x= tan e to show that sin? 20 dx. %3D (1+x*)' 4x2 (ii) Hence find in…

A:

Q: | 1283 sin(x)) cos(x)dx Az)dx = 13 Find O a No correct answer b. 26 O b.26 Ос - 26 Od 52 O e.-52

A: The integral is given by I = ∫0π212f3sinxcosxdx                            ........(1)  To evaluate…

Q: Integrals Evaluate each integral.

A:

Q: 4. 2 sin e cos e - cos e 1- sin_e + sin?e- cos? e

A: (2sinΘcosΘ -cosΘ)/(1 - sinΘ +sin2Θ -cos2Θ ) (cosΘ)(2sinΘ -1)/(2sin2Θ  - sinΘ ) cosΘ(2sinΘ -1)/(sinΘ…

Q: 4 sin? r d) lim a-0 3x tanx

A: see below the answerHere we use the L'Hospital Rule islimx→af(x)g(x) is of the form 00 then…

Q: Ex(i) Find the aln Ja that Mles fcas is Contincnity at X= I , where Cos X x to ーメ2 そa-3a+4 X =0

A:

Q: gives a value of sinh x or cosh x. Use the definitions and the identity cosh2 x - sinh2 x = 1 to…

A: 1. Given: sinhx=-34 To find the values of the remaining five hyperbolic functions. Solution: We have…

Q: 12 Hint: write secant in terms of cosine and go from there.) Find the exact value of sec (-5).…

A: Given sec(-7π12)We now split the angle into two angles of known values⇒sec(-π4-π3)We know that…

Q: S- 7- 16x? 1. dx Do not use trigonometric substitution for #1 (it is not necessary). Use another…

A:

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: Evaluate the integrals

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: A. Bernoulli's Egquation 2. (3 tan X - 2 cos y) sec?xdx + tan x sin ydy - 0

A: Explanation The equation is in the form dydx+P(x)y=Q(x)yn is called the Bernoulli's equation Now we…

Q: 22. tan?0 sec+0 d0 26. /4 sec'0 tan e de

A:

Q: sec² x 0 1+tanx If sh -TT/2 -TT/4 TT/3 TT/6 O dx In 2, then what is the value of k? =

A:

Q: 3n determine the exact value of 2 3 2, where <xsn, and cot y = where 7< ys. 5 3. If cos x 2 12 cos…

A:

Q: (i) Express -5 sih 0 + 12 cos 0 in the form R cos(0 + a), where R>0 and 0<a < n. Give the value of a…

A: Okay I am solving first question as you mentioned.

Q: Using trigonometric substitution to evaluate, 2 5² dy y√√y²-25

A:

Q: dx Using trigonometric substitution S = sin(0) + C, express the answer in terms of x. 3 (x²+x+1)7

A:

Q: Let x = 0.29 and y = 4.03. Determine the value of C when you evaluate tan(2x)dx.(Use 2 decimal…

A:

Q: 2) Derive an expression to estimate the possible error in S calculated from 1 S =-bc sin A, 2 where…

A:

Q: finda general solution, show the steps of derivation. y' sin 2pi x = pi y cos 2 pi x

A:

Q: cos*x If S(cos3x B) dx = - + C, what is the B? 4 A. - sin x С. - COSX . 1 D. 1 В. CSC X sec x

A:

Q: X=gin (20) you cos() - Aiminate thc porometer to Find a Cartesron eguatien. -Sketch gropn

A:

Q: n/2 cos x eSinx dx=? A 1-e В -е e-1 e/2

A:

Q: Let x = 0.1 and y = 4.73. Determine the value of C when you evaluate tan(2x)dx.(Use 2 decimal digit)…

A: C=3.61 I have done solution step by step in detail....go through the solution

Q: H(x) = sin(esinh~1 *) %3D

A:

Q: 5. Find all values of e 0° <e<360° if a) sin e = 0.7880 Pick a) or b) one b) tan e = -V3 %3D

A: "Since you have posted multiple questions we will solve the first question for you. If you want any…

Q: Solve for y

A: Given that : The equation is y = 4 cos x .

Q: S tan?x secs x dx 1 х + Ос none of the choices 1 -sec"x + sec*x + C + C O A B.

A:

Q: Recoll that e ošx Find S orecosx. 1/2 x sin(coi'x ) de

A: ∫012xsincos-1xdx

Q: sin“ x + cost a =1– 2 cos? x + 2 cos e

A: We can find the answer as given below

Q: Evaluate using Trigonometric Substitution: dx (16+#²)? æ(x²+16) tan-1 +C - a2+24 x(x²+24) 6 tan-1 +…

A:

Q: ouse the imProved wmethod Solve the : y ty tan X= sinzX ;ylo)=l ;h=ol

A:

Q: al Evalluate; I. cos X AX V sin x Hints sin'x+cosX-4

A:

Q: n/2 cos x esinx dx=? A) 1-e В -e с) e-1

A:

Q: n/2 cos x esinx dx=? A) e-1 e 1-e e/2

A:

Q: 2. Using trigonometric substitution, what is S x² -9 dx ? x3

A: Given integral √x^2-9 /x^3 dx

Q: 1IF Sine2-0.9, Find the valu e of Sino + Sin(e+2 + Sin(e+47

A: Our guidelines for multiple questions,answer only first question

Q: cos e - t/7, 270° < 8 < 360° sin e- tan e- cot e- 7 sec e-

A:

Q: p(x) = sin cos x Select the correct response: tan x O 1 O sin? x – cos² x 2 COS“ x -

A: Given that

Q: 6. What is value of y that is no y = sin-1 x? A. 0 С. B.

A: here we have to find the value of that is not in the range of the function y=sin-1x

Q: L:(sin x – 1) dx + ,cos x + 1) dx =? c)-1 а.) -89 b.) -91 d.) - (1 +)

A:

Q: S sin? x dx Evaluate 1+cos x

A: ∫sin2x1+cosxdx

Q: 20. A certain substitution gives S sin³x cos"x dx = S (u° - u’) du . What is n? Your answer

A:

Q: Q: Find the values of a and b so that a e-1 2-e'FT3<r<-2 ,x = -2 f(x) = {b x*-16 sin --2 <x<0 X+32

A:

Trigonometric Identities

Trigonometry in mathematics deals with the right-angled triangle’s angles and sides. By trigonometric identities, we mean the identities we use whenever we need to express the various trigonometric functions in terms of an equation.

Inverse Trigonometric Functions

Inverse trigonometric functions are the inverse of normal trigonometric functions. Alternatively denoted as cyclometric or arcus functions, these inverse trigonometric functions exist to counter the basic trigonometric functions, such as sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant (cosec). When trigonometric ratios are calculated, the angular values can be calculated with the help of the inverse trigonometric functions.