2. a) Write sin(3 – i) in the form of a + bi . b) Find all the values of (3)-in .

Q: Find sin θ and cos θ if the terminal side of θ lies along the line y = 3x in QI

A: Given, The terminal side of θ lies along the line y = 3x in QI.

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

A: Here given equation is cos 2π/3 + i sin 2π/3 = cos 60° + i sin 60° = 1/2 + i 3/2

Q: If r=In(sin2r), then dr is equal to

A:

Q: Show that the following is true. cos(X-pi/2) = sinX

A:

Q: Find the exact value of cos2 15° - sin2 15°.

A: We have to find the exact value of cos2 15°-sin2 15°Formula used :-Cos 2θ= cos2 θ-sin2θ -1

Q: Find all values of x in the interval [0, 2?] that satisfy the equation. 6 cos(x) + 3 sin(2x) = 0

A:

Q: find the four non zero terms in the maclaurin serise for sin h-lx

A: Formula Used: We will need following binomial expansion:

Q: is: The number of zeros of sin(-) is: `z-1

A: If y=f(z), then the variable z is called the input of the function, and y is called the output of…

Q: Find sin 2x, cos 2x, and tan2x if tanx = and x terminates in guadrant II. sin 2x ? cos 2.x tan 2x…

A:

Q: 4. Express the following in cartesian form. 2 2 cos 03 sin

A: Given r=22cosθ-3sinθTo express in cartesian form:

Q: PROVE that sin x = V1 – cos² x is NOT an identity. -

A:

Q: Express the 10th term of ( x1 + x2)º in terms of sinusoidal functions (sin, cos).

A: The expression is x1+x220. As we have obtained…

Q: is there a proof that cos^2t +sin^2t=x^2 + y^2 =1 ? if there is , how?

A: To prove the below statement Consider a right angle triangle as shown below

Q: Evaluate sin(In æ) dæ .

A: To evaluate the given integral.

Q: 20. What is sin 17t? а. 1 b. -1 С. О d. undefined

A:

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

A: To: Express in the form a + bi where a and b are real numbers 5(cosπ+i sinπ)

Q: 1. If z = sin2+In^, find the value of x- +y X

A:

Q: Find sin 5, given that sin x = 2 i and 0<x<5.

A: Here  sin x=14⇒cos x=1-sin2x              ⇒cos x=1-116              ⇒cos x=154 Now, sin2x2=1- cos x2…

Q: (a) Prove that Sin-1x  + Cos-1 x  = π/2 .(b) Use part (a) to prove Formula 6.

A: a) We have to prove sin-1x+cos-1x=π2 Let sin-1x=θ                                     ⋯⋯1…

Q: 5. cos A =- and sin B =, both A and B in QIl. 6. cos A = - and cos B = - 2, with A and B in QIII. 17

A:

Q: Q2/Prove that cos 17° + sin17° = tan62° cos17° – sin17°

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

Q: 4л Compute the exact value of sin( + ). Provide your answer below:

A:

Q: Q4: Prove that: cos?x – sin?x cos²x - 1- tan?x

A: We need to prove that cos2x-sin2xcos2x=1-tan2x We will use tanx =sin xcos x

Q: Show that V2 + V2 cos 2 and cos 16 and use it to find sin 16 Show that

A:

Q: B) Prove that: cos? 0 – sin? 0 1-tan? 0 =- 1+tan? 0

A: B)cos2θ-sin2θ=1-tan2θ1+tan2θRHS1-tan2θ1+tan2θ

Q: Q2/Prove that cos 17° + sin17° = tan62° cos17° - sin17°

A:

Q: find the exact value of the expressoion:   cos[sin-1(1/2)]

A: We have to evaluate the value of

Q: -1 Prove sin xdx = --1 2

A: First we will find the solution for indefinite integral ∫sin-1x dx then we will find the solution of…

Q: Prove that c) 1-tan?A -Cos 2A Htan?A

A:

Q: PROVE that sin x = v1 – cos² x is NOT an identity.

A: Topic:- trigonometry

Q: 4. Establish the identity using the sum and difference formulas: sin (m – 0) = sin 0

A:

Q: Prove that, cos20 + sin?0 = 1

A: Let a, b and c be the lengths of right angled triangle. Then by definition,

Q: sin A = 4/5 with A in QII, and sin B = −3/5 with B in QIII, find sin (A + B).

A: Given query is to find value of sin (A+B).

Q: Use DeMoivre’s Theorem to find z4 if z = 2 (cos 3π/4 + i sin 3π/4). Write your answer in standard…

A:

Q: Complete the statements.

A: a). As x→-1+, sin-1x→-π2

Q: Show that 7 sin? xdx L? cos? ædr I|

A:

Q: To evaluate sin e de , factor sin³e as (sin²e) ² sin® and let sin²0 =-(1- cos20). A True B False

A:

Q: Prove that the following identity is true.   sin4 t - cos4 t / sin2 t cos2 t = sec2 t - csc2 t

A: Given that sin4t-cos4tsin2tcos2t=sec2t-cosec2t

Q: Prove that cos(sin-x) = /I– x².

A: Given: sin-1x=cos-11-x2

Q: Express 6(cos 2pi/3 + i sin 2pi/3) in the form of a +bi

A: Here the given polar form of a complex number is 6(cos2π3+isin2π3) . Now we express the polar form…

Q: Derive the following formulas: cos 2x =1-2 sin² x

A:

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

A:

Q: Form the differenti al equati on by eliminating the arbitrary constants A and B from the equati on y…

A: Here we have the equation  y = ex (A cos x + B sin x)

Q: Prove by MSE that a. sin 90° = 1 b. cos 180° = -1

A:

Q: Prove: sin? xcos?x = - cos(4x). 8.

A: We will use various trigonometric formulas to prove the given identity.

Q: Determine 1-/[e-tt sin(2t)] 2- 23+3s)*

A: Given

Q: 33. Use addition formulas and the values of sin 0 and cos 0 for 0 = to compute sin 12 and cos…

A: Given: sin7π12, cos7π12 We know that sinA+B=sinAcosB+cosAsinB…

Q: If sin A = 4/5 with A in QII, and sin B = -3/5 with B in QIII, find sin A/2 and cos B/2

A: It is given that sin A=45, where A lies in the second quadrant and cos B=-35 where B lies in the…

Angles

In mathematics, angles constitute a very important part. Just like the concept of lines, an angle is a necessary figure that is used for measurement. How do you define its formation? It is formed when two or more lines meet at a point. The point at which two or more lines meet is known as the vertex. When the lines get inclined at this point, they do form various angles. Angles are measured from the vertex in terms of degrees.