11. The terminal side of an angle 0 intersects the unit circle at point (2. – V2). What is the exact value of sin(0)?

Q: 1 Use the Trapezium Rule, with seven ordinates, to evaluate In(sin.r+3)dxcorrect to four decimal…

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Q: Given that " = n, sin (x) dx 3 -T, what is 8 sin (0) de?

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Q: Set up a trigonometric ratio from ZH to solve for x. H U 14

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Q: In AXYZ, the measure of ZZ=90°, YX = 37, ZY = 12, and XZ = 35. What ratio represents the sine of ZX?

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Q: Given that 3 tan 4x = 1-4 sec 4x, the largest value of æ, for () < x < T, is PT radians, where p =

A: The given trigonometric equation is  3tan24x = 1 - 4sec4x

Q: 41 Write tan 36 in terms of the tangent of a positive acute angle. Select the correct answer below:…

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Q: 13-Find the terminal point  P(x, y) on the unit circle determined by the given value of t. t = −…

A: Coordinates  of the terminal point would be    x=cos -2π3, y=sin  -2π3

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

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Q: 1. Find the area of the part of a petal of the four leafed rose r = circle of radius . | cos(20)|…

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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: TO is equal to 10 TO 4. The value of 4cos -3 sec 10 tan 30

A: We will find out the required value.

Q: – sin x show that - In |sec x +c ??? %3D COS X

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Q: 1.Located in the second quadrant, determine the length of the arc created from x = -1 to x = -3 of…

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

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Q: In AXYZ, the measure of ZZ=90°, XZ = 63, ZY = 16, and YX 65. What ratio represents the sine of ZX?

A: Given that right triangle XYZin which XZ=65 , ZY=16 and XY=65we have to find sin∠X

Q: For what values of x can we replace sin x by x - (x3/3!) and obtain an error whose magnitude is no…

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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: Evaluate the expression under the given conditions. sin(0 – 4); tan(8) 4' O in Quadrant III, sin(@)…

A: sinθ-φ; tanθ=34, θ in quadrant III, sinφ=-1010, φ in quadrant IV tanθ=34 III quadrant Since both…

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: Consider the following unit Circle -By the definition of the sine function, sin(Ø)= x, -x, y, or -y?…

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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: If tan ☺ =3, T e<3T Find the exact att valce AJ sin 6

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Q: 22. Determine sin? y cos® y dy

A: Note that the reduction formula for ∫0π2cosnx dx=n-1nn-3n-2...231, if n is oddn-1nn-3n-2...12π2, if…

Q: 2. ind the length of an arc of the cycloid given by, x = a(0 + sin0), y = a(1 + cos0), Ar

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Q: 12. Explain why using trigonometric substitution with x = a tan u often involves a triangle with…

A: Consider the right triangle below with angle u , opposite side x and adjacent side a.

Q: 17) ABCD~AWYX. Which 3 trigonometric ratios are congruent to sinY? B W

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Q: 19 21 Choose the function that could be used to find the measure of the angle with the "?". sin COS…

A: Given: A right-angled triangle with hypotenuse 21 units, and a side as 19 units. From the unknown…

Q: Calculate the length of the side XY given the following data for 29°: Sin 29° 0.485 Cos 29° 0.875…

A: 1) The Tanθ is the ratio of the Opposite side to the Adjacent, where (θ) is one of the acute angles.…

Q: ind the length of the arc formed by x2 5y3 from point A to point B, where A = (0,0) and B = (25, 5).

A: Solution: The objective is to find the arc length

Q: Find sin 0, where 0 is the angle shown. Give an exact value, not a decimal approximation. 11

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Q: The angle y whose sine is -1/2 and which is in the interval [-pi/2, pi/2] is y = ?what?

A: Write the given statement in mathematical form and find the angle.

Q: For what values of x in [0, 27| does the graph of y = cos have a horizontal tangent? List the…

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Q: 119 Suppose that is an angle in quadrant 2 and that cos y = 2 %3D 169 (). Compute the exact value of…

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Q: Approximate to four decimal places, when appropriate.

A: To evaluate,

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

A:

Q: Find sin 0, where 0 is the angle shown. Give an exact value, not a decimal approximation 13

A: sin theta=opposite/hypotenuse

Q: In AXYZ, the measure of ZZ=90°, XZ = 63, ZY = 16, and YX = 65. What ratio represents the sine of X?

A: First sketch a triangle for the given measures as shown below.

Q: 1. If the angle 0 is in standard position and P(x, y) is a point on the terminal side of 0, and r is…

A: Draw the diagram according to the question.

Q: Given that cos 0 = v2, and the terminal arm i %3D nteasure of the angle in standard position?

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Q: Find the exact value of sin​(u​-v) given that sin u= 5/13 and sin v= 8/17​, with u and v in quadrant…

A: In the question we have to find sin(u-v).Where u and v are in first quadrant.

Q: 4. Apply half-angle formula to find b. sin 15° 5m C. COS a. cos 15°

A: The half-angle formulas are: sinθ2=±1-cosθ2cosθ2=±1+cosθ2   We know that the sine function is…

Q: D let cOs x ) and cos x lies below the x axis e Find sin(2x), cos(2x) and tan (ex). ) Proof the…

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

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Q: If the area inside the cardioidr= 9+9 cos 0 but outside the circle r = 4 cos 0 is A÷, then what is…

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Q: 3. Given the following definitions, draw a right triangle that fits the descriptions: sin y =K/L and…

A: siny=KL and tanθ=ZY

Q: If P(a, b) is on the unit circle whose arc léngth from the point (1, 0) is t, which of the following…

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Q: Find the derirative of Show 24 arc sin Ct?). our work ne ncally

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Q: In AJKL, the measure of ZL-90°, JL = 24, LK =7, and KJ = 25. What is the value of %3D %3D the sine…

A: Given information: In right triangle JKL in the diagram below, KL = 7, JK = 25, JL = 24, and ∠L =…

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.