Derive the cosine formula a2 = b2 + c2 – 2bc cos A and the sine formula sin A sin B sin C а b C Using dot product and cross product respectively.

Q: Write 2 cos(3t) + sin(3t) as Rcos(wt - ). |

A: Here we will write in the form of Rcos(ωt-∅),

Q: Express in the form a + bi where a and b are real numbers.

A:

Q: 13t 35л sin 18 35п 13t sin COS COS 36 18 36

A:

Q: B)Prove (cose + i sine)" = cosne + i sin ne

A:

Q: Evaluating √√9-x² dx using trigonometric substitution will lead to: 57/2 A 18 "/2 cos²0d0 35*1/2 B…

A: ANS: B

Q: Find 'an equation in X, y r Cos ☺ 25 r Sin@= - 2

A:

Q: Find the value of A. (A-B+C) + (2A + B) sin (2y) - (2B - A) cos (2y) = (4 + j3) − (6-j2) sin² (y)

A: Hint: The given equation is A-B+C)+(2A+Bsin(2y)-(2B-A)cos(2y)=(4+j3)-(6-j2)sin2y. Solve the given…

Q: Write z = 4 (cos pi/3 -i sin pi/3) in the form z = re ^ (i theta)

A:

Q: Convert r = 6(sin(0) + cos(0)) to an equation in rectangular coordinates in terms of x and y.

A:

Q: Find the sine of ZY. 26 24 10 Simplify your answer and write it as a proper fraction, improper…

A:

Q: Find the four fourth roots of  z = 81(cos 4pi/3 + i sin 4pi/3) w0=  w1= w2= w3= .  Write each…

A:

Q: Evaluating √9-x² dx using trigonometric substitution will lead to: -3 C=/2 A 18 cos²0d0 (B) 1852/200…

A: See the details solution in below

Q: Solve the cofunction of sec(3pi/10)

A: The given expression is sec3π10. Cofunction identities in radians. sec3π10= csc(π2 -…

Q: B)Prove (cose + i sine)" = cosno + i sin no

A:

Q: Find the product of z1 & Z2, leave answer in trigonometric form: 235 (cos플 + isin) & z2 =: +i sin 3…

A: We know that for  z1 = r1 cos θ1 + i sin θ1  and  z2 = r2 cos θ2 + i sin θ2 z1·z2 = r1·r2 cosθ1+θ2 +…

Q: Which of the following equations is CORRECT? O sinA cosB =1/2[cos(A -B)-cos(A+B)] O cosu-cosv= -2…

A: From the given options

Q: Use the appropriate formula to express the product sin x cos 2x as a sum or difference.

A: Given Data The product of trignometry formula is sin x cos 2x.   The general formula for the product…

Q: Find the value of the product. 3 sin37.5°cos7.5°

A:

Q: Find the velocity, speed, and acceleration of 7(t) = ( cos(3t), sin(3t), t² + 2t ) CoS

A:

Q: Make the substitution u = 7 cos e in the expression 1/V 49 - u2, and simplify the result. (Assume…

A: Make the substitution u=7cosθ in the expression 149-u2.

Q: Show that sin (A + B) + sin (A – B) = 2 sin A cos B. -

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

Q: Write the expression as a Single trigonometnic furction. cos 6x cos4x Sin6x Sin4x a Cos 12x b. Sin…

A: Explanation of the answer is as follows

Q: Q5) chang e the Po lar 2r=2+cos o.(2r-1) to Cartesian

A:

Q: Given that the characteristic equation has the following complementary solution, what are its roots?…

A: To find The roots of the given complementary solution.

Q: Evaluating √9-x² dx using trigonometric substitution will lead to: -3 A 355/20 cos²0de 0 **/2 B Ⓒ 18…

A: Evaluate using trigonometric substitution ∫-339-x2dx=?

Q: Express the number -9 in the form R(cos(0) + i sin(0)) = Re where R> 0 and 0 ≤ 0 ≤ 2TT. NOTE: Enter…

A: Exponential and Polar form

Q: Cannot solve

A: To find the value

Q: 1. In AABC right angled at B, AB=24 cm, BC=7 cm. Determine (i), sin A.cos A

A:

Q: Use the appropriate formula to express the product cos 5x/2 sin x/2 as a sum or difference.

A: Formula used:

Q: Evaluate | (1-cos3x)sin3x dx using the method of substitution a. 6. b. С. d. O b O C 115 115 157

A: As we know that the power rule: ∫xndx=xn+1n+1+C ;n≠-1   From the given problem:…

Q: Given that the characteristic equation has the following complementary solution, what are its roots?…

A: We will find out the required roots of given complementary solution.

Q: Evaluating √9-x² dx using trigonometric substitution will lead to: [/2cos²0do (A) 18 9[*/ cos²0d0 B…

A:

Q: -1+3 cos 0 = 3V3 - 1

A:

Q: Write cos(i – 4) in the form of a + bi.

A: Use the trigonometry formula for cos(A-B)

Q: Use the appropriate formula to express the product cos 7x cos 3x as a sum or difference.

A: The formula to express the product cosAcosB as a sum can be written as, cosAcosB=cosA+B+cosA-B2

Q: Find the value of A. (A-B+C) + (2A + B) sin (2y) - (2B - A) COS (2y) = (4+j3) (6-j2) sin² (y)

A:

Q: Find the product of: (a) 6(cos=+i sin) and 2 (cos+i sin) 3

A:

Q: What is the value of cos 6. а. 1 b. 2 V3 C. d.

A: Given that: cosπ6

Q: Solve the following equation in Cartesian form (r = 1 - cos theta)

A: Given:- r = 1-cosθ To find:- Cartesian form given equation

Q: Determine whether the following statement is true or false. If y = sin¹ (4x4), then = 16x³sin³ (4x4)…

A:

Q: Evaluating 9-x² dx using trigonometric substitution will lead to: A of th (A) cos²0d0 [*/ cos²0de Ⓒ…

A:

Q: How do we arrive at a formula for the product sin A cos B?

A: We have to derive an expression for sinAcosB.  We start off with the sum of angles formulae sinA+B=…

Q: Find the product zw given: z =(cos 280° +i sin 280°) and w=(cos 50° + i sin 50°) %3D A. Express your…

A:

Q: Evaluating √9-x² dx using trigonometric substitution will lead to: **/2 Ⓒ 18/¹/2 (A) sin²0d0 0 **/2…

A: See the details solution in below

Q: Write z = 2(cos 60° + i sin 60°) in rectangular form.

A: Write z = 2(cos 60° + i sin 60°) in rectangular form.

Q: Convert to rectangular form. (a) r= 4 cos 0 (b) r = 4 sin 20

A:

Q: Given that the characteristic equation has the following complementary solution, what are its roots?…

A: The given complementary solution is y=(c1+c2x)cos2x+(c3+c4x)sin2x

Q: (b) /(cos æ)* sin a da

A: