Use basic identities to simplify sin3x+cos2xsinx.   Enclose arguments of functions in parentheses

Q: Use the trig substitution x=5 sin t,  to re-write the square root sign of 25-x^2, without any square…

A: Simplification

Q: Find all values of x such that sin 2x = sin x and 0 <x< 2m.

A: sin 2x=sinx⇒sin 2x-sin x=0⇒2 sin x cos x -sin x=0⇒sin x2 cos x-1=0⇒sin x=0  or  2 cos x-1=0 sin…

Q: Use an identity to solve the equation sin (x + π/4) + sin (x - π/4) = 1 on the interval [0, 2π).

A: We will use sin(A+B)=sinAcosB+cosAsinB and sin(A-B)=sinAcosB-cosAsinB

Q: Q1. Evaluate without a calculator sin-1 (sin

A: Given,  sin-1sinπ4  We have to calculate it.

Q: Show that the following is true. cos(X-pi/2) = sinX

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Q: Express sin S as a fraction in simplest terms.

A: Topic:- trigonometry and geometry

Q: if x+1/x=2,find sin-1x

A: Given,

Q: To begin evaluating S sin*(x) · cos³(x)dx, express a. sin*x to (sin²x)²and use the identity sin²x…

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Q: Rewrite cos ( x in terms of sin(x) and cos(x) 3 -

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Q: Estimate the error if P 3(x) = x - (x^3/6) is used to estimate the value of sin x at x = 0.1.

A: Given:

Q: Use an identity to solve the equation 2cos2 x - sin x - 1 = 0 on the interval [0, 2π).

A:

Q: Differentiate the given sin (x² +1) 2 X

A: Sin(x2+1) To differentiate the given function

Q: Use an identity to solve the equation 3cos2 x = sin2 x on the interval [0, 2π).

A:

Q: solve for x so that sin[2(tan^-1(3/x))]= - 3/4

A: We have given sin2tan-13x=-34 Then,…

Q: : Find Sin 1(2-2i)

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Q: Write an algebraic formula for sin[(sin^-1(u)-cos^-1 (v)]

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Q: Q3) Use the addition formulas to derive the identity of (cos (x --): sin x ) %3D

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Q: find øif 0°&lt;ø&lt;360° ans sinø=-0.2456

A: Given,    sinø= -0.2456          where,  0°&lt;ø&lt;360°        Sign of sinø in all four quadrant…

Q: Derive the following function 7.y=sin(tan sin2x)

A: As per bartleby guidelines we only give first question answers.

Q: Evaluate: sin rv1- 4 cos² x dx. /9 – (In r)² Evaluate: dr.

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Q: If f(x) = 2 sin- (24), then f'(x) =

A:

Q: Rewrite sin ( x in terms of sin(x) and cos(x). 4 |

A: sin ( a - b) = sin a cos b - cos a sin b

Q: (b) Explain that function f(x) = 1 is not perpendicular to sin(x) or to sin(3x), but is…

A: Introduction: The inner product space is a map from the Cartesian product of vectors space V×V to…

Q: 6. When defining the inverse sine function, the domain of y = sin x is restricted to -÷<xs. a. Why…

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Q: show that there is a root of sin(x2)=e2-2.

A: To show that there is a root of sin(x2)=e2-2.

Q: Use identities to find values of sin 2x and cos 2x with the following condition. tan x = 2 and cos x…

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Q: (-) in terms of sin(x) and cos(x) 4 Rewrite sin x

A: Use formula Sin(A-B)=SinA.CosB-CosA.SinB

Q: Use an identity to solve the equation sin (x + π/3) + sin (x - π/3) = 1 on the interval [0, 2π).

A: sinA + sin B = 2sinA+B2cosA-B2

Q: Rewrite sin ( x + in terms of sin(x) and cos(x) 4

A: We know  sin(a+b) = sin(a)cos(b) + cos(a)sin(b)

Q: Rewrite sin (z + in terms of sin(x) and cos(x)

A: Recall:  sin(A+B)=sin A cos B+sin B cos A We have, A=x, B=π3

Q: Express the function below as a sum or difference of sine and cosine.    sin 4x cos 3x

A: Given: y=sin4xcos3x We know that 2sinAcosB=sinA+B+sinA-B                                         ..1

Q: what is the derivate of sin(x)cos(x)?

A:

Q: Rewrite cos ( x –) in terms of sin(x) and cos(x) 3

A: we know that cos(x-y)=cos(x)cos(y)+sin(x)sin(y)

Q: a( :). sin x Δ x2+2x-1

A: We have to solve given problem:

Q: 3 Use basic identities to simplify sin° x + cos“ x sin x.

A: sin3x+cos2xsinx This can be written in the form sinx3+cos2ssinx Now simplify this expression  So…

Q: Write f(x) = -2 sin(x) + 4 cos(x) using a single sine function.

A:

Q: Find an equivalent expression that involves functions of x alone. Зп sin 4 -

A: Given expression, sin3π2-x

Q: If f(x) = 6 sin- (x), then f'(x) =

A: We have to find solution

Q: Evaluate and show your work a. sin (π - x) + cos (3π/2 - x) b. sec3π/4csc5π/4 + tan4π/3cot11π/6…

A: To Evaluate: a. sin (π - x) + cos (3π/2 - x) b. sec3π/4csc5π/4 + tan4π/3cot11π/6 c. Tan-1(-√3)

Q: ) In(sin(3x +2))

A:

Q: Use an identity to solve the equation sin2 x - 2cos x - 2 = 0 on the interval [0, 2π).

A:

Q: Rewrite cos x in terms of sin() and cos(x) 4

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Q: Find sin (x- π/2) if cos x=0.65

A: On solving this we will get

Q: If f(x) = 7 sin - (2²), then f' (æ) =

A: We know , d/dx (arcsin(x))= 1/√(1-x²)

Q: 1. Make the substitution x = 3 sin(0) into the expression V9 – x² and simplify. Leave your answer in…

A:

Q: Write the expression as an algebraic expressionin x for x>0. a.  sec [sin-1 (x/sqroot(x2+9))]

A: Since you have asked  multiple questions in single request  so we  will be answering only first…

Q: Use the Substitution Rule to prove that∫sin2ax dx =(x/2) -(sin(2ax)/4a )+ C

A: Given:∫ sin2 ax dx

Q: Determine the domain of the function f(x) = √ (3x + 5) sin(5x).

A: Given: fx=3x+5sin5x We know that for sine function domain is R and for square root function domain…