Find a formula for tan(arcsinx), for |x| < 1-

Q: Find the exact value of the expression whenever it is defined.arcsin √3/2

A: To find the exact value of arcsin(32) we need to find the angle of sin where sin value is 32  sin…

Q: suppose x is a real number. Evaluate: sin ( arctan(x/4))

A: Given:

Q: Approximate sin 179 degrees using linear approximations.

A: Approximate Sin179°  using linear ApproximationLet x = 179° ,  a = 180°,  Hence∆x = x-a = 179°-180°=…

Q: What is the indefininte intregal of Tan^-1(3x) / 1+9x^2 .

A: The given indefinite integral is

Q: The least positive value x for which tan x= 0 is

A: Question is from trigonometry  And it is a well known fact that tan x = 0 only when x = nπ , where n…

Q: Evaluate lim cos(n+sin x)

A:

Q: Find an algebraic expression for cos(arcsin(2x)).

A: To Find an algebraic expression for cos(arcsin(2x)).

Q: 3. Find the integral of these Trigonometric functions

A: Hey, since there are multiple sub-parts posted, we will answer first three sub-parts. If you want…

Q: Verify the identity. tan (x + 0) = tan e Write the left side of the identity using either the sum or…

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Q: Sketch the graph over exactly. [0, 2π].  f (θ) = 2 sin 4θ

A:

Q: How would you graph one period of f(x)=cos3(x+ π) on paper?

A: We will find out the required graph.

Q: Define the Arcsine and Arccosine Functions?

A:

Q: Use the knowledge of the Mean Value Theorem to prove the trigonometric identity x – 1 arcsin 2…

A: In order to prove the identity, we need to consider a function and by using mean value theorem we…

Q: Use the definition of the hyperbolic sine to show that sinh x is an odd function.

A:

Q: express as an algebraic expression in terms of x. sin(arctan(x))

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Q: 2nd eg- how to derive tan^2x

A:

Q: List the x values of the discontinuities of the function below: y = In (tan²(x)) over the interval…

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Q: Find the exact value of the expression whenever it is defined.arctan 0

A: tan-10

Q: 5) Evaluate the given expression without the aid of a calculator tan[arcsin( +1 x+ 6 --)]

A: We have to evaluate the given expression without the aid of a calculator.

Q: What is the graph of the function over a​ two-period interval. y= tan 4 (x+(\pi )/(4))

A:

Q: Find all æ values on the graph of f(x) = 2x – 4 cos æ for 0 < a < 2n where the tangent line has…

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Q: Find the limit of tan(4x)/sin(6x) as x approaches zero.

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Q: -) Use a sketch to find the exact value of y = cos ( tan' Be sure to define all necessary…

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Q: Use the Secant Method to approximate the positive root of 2x²-sin=' x=0. Sketch the graph of the…

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Q: Find the exact value of the expression whenever it is defined.arcsin 0

A:

Q: Why does tan(pi) = 0? How do you get there?

A: We need to prove that,

Q: The function f(x) = 3 sin(4x)has amplitude________ and period_____

A: Given: f(x)=3sin(4x) The standard form of the equation is f(x)=Asinωx

Q: (a) Show that tan x = dx sec?x using quotient rule.

A:

Q: Sketch, on separate graphs, each of the functions : (i)sinh(x). (ii)cosh(x). (iii)tanh(x).

A: Hyperbolic functions: These functions are defined as the algebraic expressions of the exponential…

Q: Find the exact value of the expression. tan arcsin 2

A:

Q: 1 V25 81x2 xp +C WeBWorK notation for sin '(x) is arcsin(x) or asinx), for x) it's arctan(x) or…

A: Given,

Q: 17c

A: From part b, it is obtained that the graph is as shown below.

Q: What is the range of the inverse sine function y= sin- (x)? (-골, 글) A 2 2 B ( 0, π) 2'2 D [0, 1]

A:

Q: ≤ Lºin( Verify that f(x) = sin() is an odd function and use that fact to show that 0 < sin(√√x) dx ≤…

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Q: What is the period of the function f(x) = 2 sin x? %3D

A: Given f(x) = 2 sin(1/2 x) Since for any given sine function of form  A.sin(bx) the period is 2π/b

Q: Verify the identity. tan (T-0) = - tan 0 Write the left side of the identity using either the sum or…

A:

Q: Is  the sine function continuous every where?

A: we know that sine function is continuous on it's domain which we can see by graph of sine function…

Q: Find the limit of the trigonometric function.

A: The given expression is limx→0cosx-sinx-12x

Q: Find the exact value of the expression whenever it is defined.

A: We have the give expression as sin-122 As we know that, sin-1sinθ=θ   if θ∈-π2,π2

Q: Express the following as an algebraic function of x. sin(arctan(2x) + arccos(2x))

A: Question is solved.

Q: Find the arc length of the graph of the function over the indicated interval. x -vrv - 3), 1sys 9 X…

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Q: Express the following as an algebraic function of x. sin(arctan(2x) – arccos(2x))

A:

Q: g'(θ) at θ = π/3 if g(θ) = θsinθ

A: Given: g(θ) = θsinθ      , θ= π3

Q: Obtain the reduction formula for ∫tan"x dx, and hence evaluate ∫ tan5x dx.

A: ∫tannx dx=∫tann-2x·tan2x dx=∫tann-2xsec2x-1 dx      ∵sec2x-tan2x=1=∫tann-2x sec2x-tann-2x…

Q: Show that tan(arccosx) for |x| s 1, x + 0.

A:

Q: The trigonometric integral [sec² x (tan³x - 2 tan² x) dx is equal to

A: SOLUTION-

Q: 7) Find the exact value of the Tan t. %3D

A: Find the exact value of tan(π) is,             tan(π) = sin(π)/ cos(π)            We know that,…

Q: The tangent line to the graph of f(x) = sin-1(x/2) at æ = 2 Is horizontal. Select one: a. False

A:

Q: What is special about the functions ƒ(x) = sin-1 (1/ sqrt(x2 + 1))  and g(x) = tan-1 (1/x)?…

A: Given functions are

Q: Find the period of the function y = 7 tan 2 x

A: Consider the function, y=7tan2x Comparing the given function with standard function, y=AtanBx+C+D…

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.