7. tan(3 + 4i)

Q: Prove: sin (2 cos x)= 2x1-x² %3D

A:

Q: 6. Write [2(cos15°+isin15°)J in rectangular form. (c) 4+4i (d) 4/7 + 4i/7 (a) 3+3i (b) 3/2 + 3i/7

A: Distribute the exponent 3, then for the polar part 3 will multiply with the angles.

Q: Rewrite cos (2 tan '4u) as an algebraic expression in u.

A: We know that  cos2α = 1-tan2α1+tan2α

Q: 3. Which is true in any AABC? bsinB a. a = sinA sinB b. C = bsinc csinB c. b = sinc d. none of the…

A:

Q: .2 -If tan -1 = 0, then prove that x2 sin 2 a. %3D

A:

Q: 6. Use a special right triangle to write tan 60° as a fraction. a. с. 1 1 b. d.

A: To find tan60°

Q: 5. What is the exact value of tan 195°? O 2 - V3 2 –

A: Using advanced trigonometric identities we can solve for tan 195o

Q: 2. Expand using a double angle formula. a) tan 5x b) -10cos 40x

A: Solving the problem with the using of double angle formulas.

Q: Evaluate and write your answer in a + bi form. [3(cos 82° + i sin 82°)]³ = Round to two decimal…

A:

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

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

Q: by using the triangle method, Show that cos (21an n+1 %3D n2+1 n-1

A:

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

A:

Q: Rewrite 4sin(×)as A sin (×+θ) A= Θ=

A: Given,           4sin(x)

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

A: we have z = 12cos4π3+ isin4π3    Now 4π3= π+π3 hence z = 12cosπ+π3+ isinπ+π3               =…

Q: Find the solution(s) for theta. -4 tan 0 = 4V3 O (120, 300} (30, 120, 210, 300} O (120} (210}

A: We can solve as follows

Q: A Show that : tan" [ ica-a)' (2ta)) -i 2

A: Let ax=eiθ. So: tan-1ix-ax+a=tan-1i1-ax1+ax                         =tan-1i1-eiθ1+eiθ…

Q: 18. Express the following in simplest form: (3+ 4i)?(3 – 4i)²

A:

Q: Let , = cos-+i sin and z, = cos-+isin 6 Express in the form : =a+bi

A:

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

A: To express: The expression 3cos3π2+isin3π2 in the form of a+ib. Given: The expression is…

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: b. Express the following quotient in the form a + bi. 2[cos 345° + i sin 345°] 5 [cos 120° + i sin…

A:

Q: Find the four fourth roots of z = 625( cos + i sin 3 Write each root in standard form. 3

A: To find four fourth roots ofz=625(cos2π3+isin2π3)

Q: 9. Evaluate. Give the exact answer, not a rounded off decimal. a. tan−1 (√3) b. sec (sin−1 ( 5 13))

A:

Q: 5. [10] Use DeMoivre's Theorem to expand [4(cos 60° +i sin 60°)]". Write your answer in a + bi form.…

A:

Q: 7. In AABC, mZC = 90, AC = 6, and AB = 10. Find tan A.

A: Solution-

Q: 3b) Compute tan 6. An exact answer is required.

A:

Q: Evaluate and write your answer in a + bi form. [3(cos 68° + i sin 68°)]° - Round to two decimal…

A: De moivre's theorem states that cosθ+isinθn=cosnθ+isinnθ

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

A: 20cos11π6+ i sin11π6

Q: Show tkat cos (2 I +x

A:

Q: Use De Moivre’s theorem to write (cos π/5 + i sin π/5)^5 in the form of a +bi

A:

Q: A. Let tan u = 3 and cos u < 0, find the exact values 1.tan 2u 2. tan u/2 3. sin 15

A: Given: tanu=3 To find: tan2u tanu/2 sin15

Q: 2 (cos 150° + i sin 150°

A: The given complex number is in Polar form, so we covert it into Cartesian form by using the…

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

A:

Q: 10. L{ cos (8t + 2) } (entry # 71)

A: To find  L{cos (8t+2)} we shall use  the following formula  1.  cos (A+B)=cos (A) cos(B)-sin (A)…

Q: Write the expression in the standard form a +bi. 元 V2 cos -+ i sin 6. 6. 元 V2 cos +i sin 6. - 6.

A: write the given expression in the Eulers form Use the rule of surds Again transform the expression…

Q: 1-tan20 = 1- 2sin?0 1+tan20

A: 1-tan2θ1+tan2θ=1-2sin2θ Formulas 1+tan2θ=sec2θ1-cos2θ=sin2θ 1secθ=cosθ

Q: Find the four fourth roots of z = 16( cos + i sin 3 Write each root in standard form. Wo = W1 = W2 =…

A: We will use the De-Moivre's theorem to find out the 4th roots of the complex number.

Q: Use De Moivre's theorem to simplify the expression. Give the answer in the form a + b i. [5( cos 30°…

A:

Q: 5)Use De Moivre's theorem to simplify the following a)(cos 20+i sin 20)(cos 50+i sin 50)

A:

Q: 3 cos- + isin 6. 6.

A:

Q: V125 cos- jsin 11 - | 11 Simplify . Express answer in rectangular form. 5 cos 47 + j sin 11 11

A: Rectangular form of the complex number

Q: Use the given triangles to evaluate the expression. Rationalize all denominato 30 45° 2 1 45° 60°…

A:

Q: z=[square root of 2(cos 3pi/4+i sin3pi/4)] write the expression in a+bi form

A: According to Euler's formula eix = cos x + i sin x

Q: Use Demoivre's Theorem to find the fallowing- answer in Standard form. your 2 eis 20 Write

A: Given (√2 cis(9π/20))5 Using demoivre's theorem we can write Zn=rn cisntheta  =(√2)5 (cis5(9π/20))…

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: Determine the guadrant in which the terminal side of 0 lies (a) cos 0 0 (Choose one) (b) sin 0 < 0…

A: Given that  A) cosθ&lt;0 and sinθ&gt;0 b) sinθ&lt;0 and tanθ&lt;0

Q: Express the following quotient in the form a + bi. 2[cos 345° + i sin 345°] 5 [cos 120° + i sin…

A: We will evaluate and find in a+ib form as shown below

Q: photo is attached

A:

Q: Evaluate and write your answer in a+bia+bi form. Round your decimals to the nearest tenth.…

A: