Thread: Trigonometric and Hyperbolic Identities

Anyone help with the answer to the following questions:

Question 1 - Using Maclaurin’s series find the first 4 terms of the expansion of Sinh(2x)

Question 2 - Review the expression 5.5 Cost + 7.8 Sin t and solve for t for values in the range 0 ≤ t ≤ 2 π rad; 5.5Cost + 7.8 Sin t = 4.5

Question 3 - An oil company drills a well 10kms deep. Estimate the total cost of drilling if the cost is £20 for drilling the first metre with an increase of £3 per metre for each succeeding metre

Can you show us what you've tried?

Question 2.2 - Hence solve for t for values in the range 0≤ t ≤ 2π rad: 5.5 Cost + 7.8 Sin t = 4.5:

Answer; 9.544Sin(t + 0.614) = 4.5

Sin (t + 0.614) = 4.5
9.544

t + 0.614 = Sin-1 [4.5]
[9.544]

Therefore; t = Sin-1 [4.5] - 0.614 and t = 27.517°,152.48°
[9.544]
Question 2 - Review the expression 5.5 Cost + 7.8 Sin t and solve for t for values in the range 0 ≤ t ≤ 2 π rad; 5.5Cost + 7.8 Sin t = 4.5


Answer; ƒ(x) = Sinh x ƒ(0) = Sinh0 = e° - e° = 0
2

ƒI(x) = Cosh x ƒI(0) = Cosh 0 = e° + e° = 1
2

ƒlI(x) = Sinh x ƒII(0) = Sinh 0 = 0

ƒIII(x) = Cosh x ƒIII(0) = Cosh 0 = 1

ƒiv(x) = Sinh x ƒiv(0) = Sinh 0 = 0

To plot the results into Maclaurin’s Series gives; (2x for x)

So; Sinh 2x = 0 + 2x(1) + (2x)2 (0) + (2x)3 (1) + (2x)4 (0) + (2x)5 (1)
2 3 4 5

Therefore; Sinh (2x) = 2x + (2x)3 + (2x)5 + …………
3 5

Guys, Please note some of the numbers where they should have been over each other i.e 4.5 have moved
9.544