Evaluating an Inverse TrigonometricFunction In Exercises 77–80, find the exact value ofthe expression.77. arcsin(−1)78. cos−1 179. arccot √380. arcsec(−√2)

Q: cot 20 = csc0– 2 sin @ 2 cos 0

A: on solving this trigonometry problem we will prove ,

Q: cscx-sinx=cotxcosx When using trigonometric identitities to prove if true, can you get an…

A: Proof:

Q: Evaluate: fx sin 2x? dx

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Q: 2

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Q: Find the exact value, in radians, of the expression. arcsin(0) = (Type an exact answer, using n as…

A: The arcsin is the inverse sine function.

Q: evaluate using the suggested method.

A: Use Pythagorean identity to convert into sec

Q: Graph the pair of functions y = tan-1 x and y = -2 tan-1 x in the same viewing rectangle. Use your…

A: To plot  y = tan-1 x and y = -2 tan-1 x in a same rectangle.  And to comment on the relation of the…

Q: Verifying a Trigonometric Identity InExercises 57–60, verify the identity.

A: tan(sin-1x) = x/√1 - x2   Let sin-1x = y               x = siny   LHS = tany   RHS = x/√1 - x2…

Q: Using a Calculator In Exercises 59–62, use acalculator to evaluate the trigonometric function.…

A: To evaluate the trigonometric function. 59. sin106°. Evaluating the value of sin106°.…

Q: Using an Inverse TrigonometricFunction In Exercises 39–44, use aninverse trigonometric function to…

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and…

Q: Using reciprocal identities how do you solve this problem? is it solvable? Cosx - Secx = -SinxTanx

A: Given that an trigonometric equation:

Q: Integrate the equation using the method in trigonometric

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Q: proving identity by steps with rules (1+tan2x)cot2x=csc2x

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Q: Think About It In Exercises 67–70, explain why theequation is not an identity and find one value of…

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

Q: Verify the identity algebraically. Use the table feature of a graphing utility to check your result…

A: The given identity is 1+sin θcos θ+cos θ1+sin θ=2sec θ

Q: ollowing when trigonometric substitution is used?

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Q: Verify the identity algebraically. Use the table feature of a graphing utility to check your result…

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Q: Verifying a Trigonometric Identity InExercises 57–64, verify the identity.

A: Draw the diagram to represent the polar coordinates of a point in a cartesian plane. Polar…

Q: Sin +Sin!

A: sin-1110+sin-115=π4

Q: Verify the identity algebraically. Use the table feature of a graphing utility to check your result…

A: Given: To verify: The given identity.

Q: Verify the identity algebraically. Use the table feature of a graphing utility to check your result…

A:

Q: Verify the identity algebraically. Use the table feature of a graphing utility to check your result…

A: The given identity is

Q: Integrate using the method of trigonometric substitution. Express the final answer in terms of the…

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Q: tan x-sin x Simplify the expression using sin x fundamental identities.

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Q: sin aX

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Q: Verify the identity algebraically. Use the table feature of a graphing utility to check your result…

A: LCM (least common multiple)  tan x = sin x / cos x cot x = cos x/ sin x  Also, tan x * cot x = 1

Q: Trigonometric Substitution In Exercises 59–62,use the trigonometric substitution to write the…

A: Our Aim is to write algebraic equation as a trigonometric equation of θ,where -π2 <θ< π2,…

Q: How are the inverse trigonometric functions defined? How can you sometimes use right triangles to…

A: Inverse trigonometric function:It is defined as that the anti or arcus function of the function is…

Q: Verify the identity algebraically. Use a graphing utility to check your result graphically.…

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Q: Error Analysis Describe the error.sin θcos(−θ) = sin θ−cos θ= −tan θ

A: Error Analysis Describe the error.  sinθcos-θ=sinθ-cosθ=-tanθ

Q: arcsin sin 4 %3D (Simplify your answer. Type an exact answer, using t as needed. Use integer numbers…

A: we have to find the following

Q: Explain the difference(s) between solving a trigonometric equation and proving a trigonometric…

A: To state the difference between solving a trigonometric equation and proving a trigonometric…

Q: Evaluate the definite integral of the trigonometric function. Use a graphing utility to verify your…

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Q: 1+cotx_ 1+sin 2x 6. cotx-1 %3D cos 2x

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Q: Use a calculator to approximate the value of the expression, if possible. Round your result to two…

A: TO FIND THE VALUE OF arc(-0.83)

Q: Find the values of the trigonometric functions from the given information. Given csc θ= -sqrt26/5…

A: Given:

Q: sin'(-x) = - SI

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Q: How do I subtract (sinϴ-1)/(cosϴ) - (cosϴ)/(sinϴ-1). Show work

A: We have given expression to subtract  Let, y=sinθ-1cosθ-cosθsinθ-1 y=sinθ-12-cos2θcosθsinθ-1 Using…

Q: X- sec x sin'x =COS

A: Solution of the problem as follows

Q: Verify the identity algebraically. Use the table feature of a graphing utility to check your result…

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Q: Using a Calculator In Exercises 75–90,use a calculator to evaluate the trigonometricfunction. Round…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: Write the composed trigonometric function sin (arctan x)sin (arctan x) in terms of x. Explain your…

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Q: Using Inverse Properties In Exercises45–50, find the exact value of the expression,if possible.45.…

A: Since you have posted multiple questions, as per our policy we will answer first question. Please…

Q: Prove the identity using trigonometric identities/definitions and algebra:

A: We have to prove the given trigonometric Identity.

Q: Application of Mean Value Theorem: 4. Prove the identity: sin² x + cos² x = 1, using the Mean Value…

A: The given identity is sin2x+cos2x=1 Let the right hand side of the function, sin2x+cos2x We know…

Q: tan(sin (-)), What is the exact value of cos (tan-(1)) Enter your answer, as a simplified fraction,…

A:

Q: 2 tan x sin 2x 1+ tan? x

A: To prove:- 2tanx1+tan2x=sin2x

Q: Integrate using the method of trigonometric substitution. Express the final answer in terms of the…

A: In this question we have to Integrate using the method of trigonometric substitution.

Q: se oda

A: We have to evaluate the integral.

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.