15 Find the exact value of the trigonometric expression given that sin(u) = - - where 37T/2

Q: a. Express x = --3-8ż in its trigonometric form r (cos(0) + i sin(0)) with 0 ≤ 0 < 2. Give your…

A: a) x=-3-8ib) 2+5i2+2i

Q: Use Newton's method to approximate a root of the equation cos(x² + 4) = x³ as follows. Let 1 = 2 be…

A: See the details solution in below

Q: Find sin e and cos e if the terminal side of 0 lies along the line y = 3x in QI. sin e - cos 8

A: Given: The equation of the line is, y=3x. The objective is to find the value of sinθ and cosθ.

Q: Eliminate the parameter t from the following. x = cos t − 2, y = sin t + 5

A:

Q: 4-If y= cos 8t , find the frequency (w) and the fundamental period(T.) 5-If: y = (sinx+1) (cosx+1)'…

A: We know that, The fundamental period(T0) of cos(x) = 2.pi                            if cos(ax) = (…

Q: 1. Find the exact values of sinh (0) and cosh (0) using their definitions.

A: Sinh x=ex-e-x2∴ sinh0=e0-e-02=1-12=0∴sinh0=0      cashx=ex+e-x2∴cash0=e0+e-02=1+12=1⇒cash0=1

Q: 2. Find the exact value of sin(a + B) under the given conditions. 5 tan a = 12 코T< a< 프, sin ß = -,…

A:

Q: 13. Evaluate the function. Give the exact value. cos (tan (V3) -1 cos(arctan( v3% )= 0.5

A: We have to find out the value

Q: 16. Calculate (sin 0 , 0 , cos 20) d0.

A: ∫0π&lt; sinθ,θ,cos 2θ&gt;dθ

Q: If x = 3 sin(0), then а. V9 + x? cos(8) 3 b. cos(x) Vx2 + 9 C. tan(x) d. cot(x) = 3 || е. sec(x) 3 O…

A:

Q: 1. Find the first derivative of the given trigonometric function 1 z = 4cos?. 2

A:

Q: Find sin(2x), cos(2x), and tan(2x) from the given information. 8 sin(x) = x in Quadrant I %3D 17…

A:

Q: */10 S sin(10z) arctan(sin 5x)dr = ? a)10(7 – 2) - 2 b)- 5 ) 5 (т — 2) T - 2 d)- 10 Ол - 10

A:

Q: 1. f/² sin () cos (+) sin (²) d dx (Consider initially the first 2 terms)

A: We have to use the formulas for 2sin(A)cos(B)-sin(A+B)+sin(A-B) and 2sin(A)sin(B)=cos(A-B)-cos(A+B).…

Q: 7. d. cos 0 cos 20 + sin 0 sin 20 = V3 over 0, 2t)

A: We know the sum identities: sin(a+b) = sina.cosb + cosa.sinb sin(a-b) = sina.cosb – cosa.sinb…

Q: (B): Find the tangent equation to the curve y = sin² x at point x = 7. (C): Solve the following…

A:

Q: 1. Find of the trigonometric function: dx y=−10x + 3 cosx

A: Derivative of Cosx is -Sinx

Q: 4 5 Points ntegral of sin-cos-sin0 de has the form (e) +C. What should be the value of e =0?

A:

Q: 18. sin³ x cos x dx

A: Here we will use substitution method for solving this problem

Q: 3 Find sin 2x, cos 2x, and tan 2.x if cos.x = and x terminates in quadrant II. V10 sin 2x %3D

A: given

Q: 1. ² sin() cos() sin(x) dx (Consider initially the first 2 terms)

A:

Q: 11. Find if y= cos(x) A. 2x sin(x) B. -x sin(r) 12. Differentiate: y=x cscx A. y' = cscx(1+x cot x)…

A: we have to differentiate the given equation . y=ex3

Q: 16. i) Find in radians, the general solution of the equation sint + sin30 = sin20. ii) Given that…

A:

Q: 1+ sin 0 . Verify cos O 2 sec e Cos A 1+ sin A

A: Our Aim is to verify 1+sin θcos θ+cos θ1+sin θ=2 sec θ -(i)

Q: When t = 0, AP = ..... so sin t will begin at a value of 0. As t increases from 0 to 7T/2, sin…

A:

Q: f/² () sin cos (sin (²) dx (Consider initially the first 2 terms)

A: To evaluate: ∫0π2sinx3cos4x3sin2x3dx Let I = ∫0π2sinx3cos4x3sin2x3dx We know that  sinxcosy =…

Q: Eliminate the parameter t from the following. x = sin t − 3, y = cos t − 2

A: Eliminate t by squarring

Q: 1) Using the formula: cos(x + y) = cos x cos y - sin x sin y, prove in steps that: cos? x = 1+cos 2…

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: 1 and tan(t) > 0, find sin(t) and cos(-t) 3 If cos(t) sin(t) = cos(-t) =

A: Given:cost=-13sint=?cos-t=?Formula:sint=1-cos2tcos-t=cost

Q: Find an equation for the line tangent to the curve at the point defined by the given value of t. x…

A:

Q: 15 Find sin 2x, cos 2x, and tan 2x if cos.xr= and x terminates in quadrant IV. 17 sin 2x cos 2x !!…

A:

Q: 1- cos(0) (d) de sin (0)

A: We have to find integration

Q: 24 and cos(x)= 25 7 what is the vaule of tan(x) 25 If sin(x)= ? z,

A: According to the tangent identity, tan(x)=sin(x)cos(x). We know the value of sin(x) and cos(x), so…

Q: 39. cos (T + x) 40. sin (2m- xr) 學一) 37T 42. cos 41. sin -

A:

Q: 10. Evaluate cos x sin² x dx

A:

Q: ♫♫¹⁄² sin (*) cos (*) sin (²) dx (Consider initially the first 2 terms)

A: Solving the definite integral.

Q: 1. Match th A. Sin В. Cos С. Tan

A: As per the guideline i can answer only first question for you, more than one answer leads me towards…

Q: How do you solve this?

A: Given that cos x = 1/3 and x is in the interval (0, π/2).sin y = 1/2 and y is in the interval (π/2,…

Q: 4. y = Arc tan² x³ 5. Ø = Are cot 2x

A:

Q: 18. The value of sin (7 +2) is equal to sin a cos z cos z - sin r

A: 18)

Q: 4. Use Gamma function to evaluate the integral: sin? (40) cos (20)d0.

A:

Q: cos(j. T/2) COS COS

A:

Q: When a pendulum 0.5 m long swings back and forth, its angular displacement O from rest position, in…

A: Given    Diagram we have a triangle with the vertical angle as Ø, the hypotenuse 50 cm (the…

Q: 1 3. a) Verify that sin x cos x = tan x--- π for the value x =-. 4 Ls Sin 4cos 4 2.s TanT/4-Y2 しS…

A: We can use the concept of trignometrical ratio in order to solve the given problem.

Q: Find the exact simplified value.

A:

Q: 3. y³x2 – cos- sin x² + esin x = 1 y DIFFERENTIATE THE GIVEN

A:

Q: * /2 2 sinh (sin 0) cos 0 d0

A:

Q: I. Determine the exact values of each of the indicated trig functions for the problems below 8. sin…

A:

Q: 3) Find the exact value of cos(a + B) under the given conditions. V5 0< a < sin ß = - -< B < 0 4 TC…

A: We know thatcosα+β=cosα cosβ-sinα sinβ

Vertices Of An Ellipse

In the study of the conic section of the geometry, An ellipse is a plane curve surrounding two focal points, or foci where the set of all locus of points in the plane has their sum of the distances to the two foci is constant. On the ellipse curve, it is the intersection point of the main axis. In an ellipse graph, the center of the axis is the midpoint of the line segment connecting the foci. The major axis is the line section that runs through the ellipse's foci, while the minor axis runs through the middle and is perpendicular to the major axis.. The ellipse has two endpoints on the major axis which are known as the vertices (in plural), vertex in the singular. The equation of the major axis is 2a, the equation of the minor is 2b and the distance between the major axis and minor axis is 2c. The semi-major axis has a length of a and the semi-minor axis has a length of b. The ellipse's vertices are determined by the elliptical orbit's equation and graph.