By using the addition formula derive the identity of the function sin (x -), then choose the correct answer:

Q: Is sin-1 x the same thing as1/sin x?

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Q: When you simplify, Csc e ( Csc 0 - Sin 0) , it is equal to :

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Q: Use a calculator to compute sinhx and coshx for x = -3, 0, 5.

A: We use a calculator to find the values.

Q: Reduce sin 0 to an expression involving only function of multiples of 0, raised to the first power.

A: Given, sin4θ  We have to reduce sin4θ to an expression involving only function of multiples of θ,…

Q: tan(t) Simplify sec(t) – cos(t) to a single trig function.

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Q: simplify sin 2x/1-cosx   Not sin^2x its sin2x

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Q: The suitable substitution to evaluate sin24(x + 2) dx is

A: Proceed as shown below...

Q: Find ø if, 0°<ø<360° and sinø=-0.2456

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Q: If you need to review them, here is a link to the DQ Instructions. Show and briefly explain your…

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Q: Use a calculator to solve the equation tan x = -5, correct to four decimal places, on the interval…

A: the given equation is tanx=-5. we have to find the solution of the given equation on the interval…

Q: a) Simplify sin 2 tan in terms of x using triangle method.

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Q: Use inverse functions where needed to find all solutions of the equation in the interval [0, 27).…

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Q: Use the Quotient Rule to differentiate the function f(x) = (tan(x) − 1)/(sec(x)   Simplify the…

A: Given:

Q: For sin3x+sinx=0,sin⁡3x+sin⁡x=0, use a sum-to-product formula to simplify the equation and then find…

A: Known fact: sinC+sinD=2 sinC+D2 cosC-D2

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

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Q: Use an identity to solve the equation on the interval [0,2x). sin 4x cos x- sin x cos 4x = 2

A: Given: sin 4x cos x -sin x cos 4x =22

Q: By using the addition formula derive the identity of the function sin (x -), then choose the correct…

A: Given the given function is sinx-π2. Apply addition formula sinp-q=sinp cosq-cosp sinq.

Q: if sec 0 + tan0 = x,obtain the value of sec O,tan0 and sin0

A: We can solve this as per equation by using trigonometry formulas

Q: Solve the equation sin 3x + sin x + cos x = 0 on the interval [0, 2π). Do not use a calculator.

A: Given: sin3x+sinx+cosx=0, x∈[0,2π) we know that sin3θ=3sinθ-4sin3θ

Q: Find an equivalent expression for sin 4x in terms of function values x sin 4x =

A: power series of f(x) about x =a is  f(x) = ∑h=0∞ fn(a)n! (x-a)n ------- (*)

Q: Solve the equation on the interval [0, 27). tanx sinx = tanx

A: Period of the tangent function tan x is π. Period of the sine function sin x is 2π. If we have the…

Q: Find given - cosx sinz

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Q: 6. sin(tan¬1 x)

A: Use inverse trigonometric method

Q: If x=2 tan θ ,express sin(2θ)as a function of x.

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Q: Express the difference sin 11x - sin 5x as a product. If possible, find this product’s exact value.

A: Given,          sin11x-sin5xWe know that,             sina-sinb=2cosa+b2sina-b2

Q: . Evaluate sin (x) cos(x)dr using an appropriate substitution.

A: According to our answering guidelines we can only answer one question at time, therefore I am…

Q: Express sin 2θ in terms of x = sin θ.

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Q: Verify the identity (sin x + cos x)² = 1+ sin 2x by converting the left hand side to the right. Give…

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Q: If x = 4 tan θ, express sin θ in terms of x.

A: Given that: x=4tanθ To solve the given trigonometric function,…

Q: Which expression is equivalent to sinβcscβsecβ for all values of β for which sinβcscβsecβ is…

A: According to reciprocal identity csc x=1sin x

Q: Since the function y=cosx and y = cosx are inverse functions, why is cos cos not equal to 2 Explain…

A: cos(-x) = cos x

Q: Use inverse functions where needed to find all solutions of the equation in the interval [0, 27).…

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Q: I am very confused about this concept. Any help would be great.   Thanks much.

A: Given expression is Let Plugging the value in the expression:

Q: If tan(x)=12/11(in Quadrant-I), find cos(2x)=

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Q: cos(pi/2 -x)=10/11,

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Q: Show that sin 2x Þ 2 sin x by substituting 30 degree for x and then simplifying both sides.

A: To prove: sin2x≠2sinx For x=30°

Q: Solve the equation on the interval 0≤θ≤2π tanθ=-(sqrt)2 sinθ

A: For solving this trigonometric equation, we have to write the given equation in factored form and…

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

A: Given expression, sin3π2-x

Q: Simplify 3 TT sin-(sinx) if TSXS 2 - -x- T ーX π-X x- π

A: Given, To solve  sin-1(sinx)  if π≤x≤3π2

Q: tan x = 2 cosx tan x

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Q: Find the exact function value. 3n sin 4

A: We have to find the exact function value for sin-3π4.

Q: Write sec x in terms of sin x.

A: Using reciprocal identity we know sec x = 1/cos x

Q: tan(sin'x) is ... The simplify of

A: Given expression is Let us suppose Now, Therefore,

Q: Use the addition formulas to derive: cos (x -) = sinx

A: The given equation is cosx-π2=sinx

Q: Simplify tan ¹(− ª) to a single trig function using the sum or difference of angles identity. 2

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Q: If x = 4 tan(θ), find sec(θ) and sin(θ) in terms of x.

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Q: State the period length of the function f(x) = -4 sin (27x).

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Q: If csc(x) = 3, for 90° < x < 180°, then sin () - cos () ||

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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.