12. Explain why using trigonometric substitution with x = a tan u often involves a triangle with side lengths a and x and hypotenuse of length x² + a².

Q: Consider the given right triangle with legs of length x cm. and y cm. and angle O radians. If x is…

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Q: 1. Evaluate √2 √4x² dx using a trigonometric substitution.

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Q: (5.)Given that sec(x) = 4 and csc(y) = -3 and both x and y are in the fourth quadrant, find tan(x +…

A: Given, sec(x) = 4 and csc(y)=-3. Here, angles x and y are in the fourth quadrant, so cosine and sec…

Q: 2- In order to read his book, Stephen uses a pair of reading glasses. When he bolds the book at a…

A: Solution

Q: Use Figure 22 to find all angles between 0 and 2π satisfying the given conditions.

A: We use the quotient property of trigonometry

Q: D?/if w= Cos (X+y)+Sin (X-y) Show that

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Q: Suppose y = sin x. %3D What y-value corresponds to an X-value of 37? 2

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Q: B) 1- Given that a = sin Find cos x, tan x, cot x, secx and csc x ?

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Q: 3. Suppose that sin r =, x lies in quadrant I, and sin y = 3 and y lies in quadrant II, find sin(x +…

A: Given: sinx=45, x lies in quadrant I. And siny=1213,y lies in quadrant II. We know that, In quadrant…

Q: 5 is a point in Quadrant II lying on the unit circle. Suppose that x, 13 Find x. Write the exact…

A: As this point lies on unit circle. So put this point in equation of unit circle and get required…

Q: How can we find x using SohCahToa? sin 34 = %3D y cos 34 = tan 34 = 34°

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Q: To explain why, for any acute angle u, it is impossible for sec theta =  1/2

A: To show:  It is impossible for sec theta =  1/2

Q: 1 dr r/1+ x6 (use trigonometric substitution) 3.

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Q: Verily the icentity. sin 6x + sin 4x = tan (5x) cos 6x + cos 4x Stort eida and

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Q: What angle does the tangent to the curve y(x) = sin? (x/9) + 15sin(x/9) at x = 9n make with the…

A: The tangent to a curve is given by dydx. we are given that y(x)=sin2(x9)+15 sin(x9) then dydx=29…

Q: 24 Suppose that x, is a point in Quadrant IV lying on the unit circle. 25 - Find x. Write the exact…

A: Given that, The point x, -2425 is 4th quadrent and lies on the unit circle. So we have to find the…

Q: Let P(x, y) be the terminal point on the unit circle determined by t. Then sin(t) = , cos(t) and…

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Q: 8. Suppose that x, is a point in Quadrant IV lying on the unit circle. 17 Find x. Write the exact…

A: Equation of circles x^2+y^2=1 Since (x,-8/17) lies on unit circle.means  then satisfies equation…

Q: 2. Give the values of the six circular functions of the standard angle 0 generated by an arc whose…

A: I have solved the question 2 for you as we can solve one question in one session. f you want the…

Q: (a) sin(rxy) = x + y?

A: I am going to solve the given problem by using some simple caculus to get the required result.

Q: Find dr 0Y-- の 3. Cosr+ Cot O =r

A: Solution:-

Q: Find mZW to the nearest tenth of a degree. W 11 in Y 3 in X mZW =

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Q: 3. Using the fact that sin 2a = 2 sin a cos a, and the fact that 0 = 2a, rewrite the area of the…

A: As per our guidelines we can answer only 1 question so kindly repost the remaining questions…

Q: equation o4 whose curuature +ind an is K = % .

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Q: 1) Evaluate. x cosh ax dx

A: As per guideline we have to solve one question

Q: For (a), how did cot y become tan y?

A: a). given  dydx=cotx cotydy= (cotx coty)dx1cotydy=cotx dx integrating on both sides we get…

Q: For what values of a and b is sin bx tan 2r lim 0?

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Q: Graph the limaçon. Oval limaçons   r = -2 + sin u

A: A Cardioid is a curve traced out by a point on the circumference of a circle rolling around another…

Q: 3. Suppose that is a point in Quadrant IV lying on the unit circle. Find y. Write the exact value,…

A: Given: The point 35,y is in quadrant IV lying on the unit circle.

Q: What are the (x, y) coo

A: we can find the coordinates using the trigonometry- x = rcosθ = cos(2π/3) = -0.5 y = rsinθ =…

Q: Give an example to justify that sin (A + B) is not equal to sin A + sin B. Limit A and B to special…

A: Special angles are those angles at which the values of the trigonometric ratios are known. For…

Q: find area Inside the circle r = 4 cos 0 and to the right of the vertical line sec 0

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Q: 16. Determine So sin x cos x dx

A: First simplify then integrate

Q: 01: Find the angle (y) between the tangents lines of the line r = 3 sec 0 and the cardioid r = 4(1 +…

A: Solution is given below:

Q: Suppose that y is an angle with cOs y 4 and y is not in the fourth quadrant. Compute the exact value…

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Q: What angle does the tangent to the curve y(x) = sin² (x/9) + 13sin(x/9) at x = 9n make with the…

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Q: 2. What is the period of the trigonometric function given by f(x) a. 플 b. 2π C. T d. 3 = 3sin(2x)?

A: This question is based on trigonometry function

Q: 5. Find the length of one arch of the cycloid x = sin and y = 1- cos 0

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Q: By using trigonometric substitution そる x = 2 tan A 4+1

A: see 2nd and 3rd step.

Q: Use Figure 22 to find all angles between 0 and 2π satisfying the given conditions.

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Q: Use Definition II to explain why, for any acute angle u, it is impossible for sin u = 2.

A: Given:  sin u=2Since sine function is bounded between…

Q: S(1 + cot²x) tan x dx

A: Given ∫1+cot2x tanx dx It is simplified as follows: ∫1+cot2x tanx dx=∫1+1tan2x tanx dx=∫tan2x+1tan2x…

Q: Suppose that y is an angle with tan y = 11 and y is not in the fourth quadrant. Compute the exact 9.…

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Q: 1 and which is in the interval [0, n] is y = 2 The angle y whose cosine is- radians.

A: Given, cos (y)=-12  where 0≤y≤πEvaluate y

Q: s = 12.5 e = 320° %3D Radius: Central angle: Length of the arc:

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Q: 4. Write an equivalent expression for sin*(x) that does not contain powers of trigonometric…

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Q: 2 of 2 + Automatic Zoom: 13. Find the value of x and classify the triangle. A. X = 34, Acute B. x =…

A: Hi, As per Bartleby rules we are supposed to do only one question at a time. Kindly repost other…

Q: 28 In the diagram below of circle O, secant ABC and tangent AD are drawn. 12.5 C

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