Hyperbolic Functions

Question 1

Define sinhx, coshx and tanhx.

Answer 1

Question 2

Define cosechx, sechx and cothx.

Answer 2

Question 3

Sketch y=sinhx

Answer 3

Question 4

Sketch y=coshx

Answer 4

Question 5

y=tanhx

Answer 5

Question 6

Hyperbolic identities rule.
(Using osborn’s rule)

Answer 6

Hyperbolic identities are identical to trig identities but every time sin^2x appears, put a negative in front and turn into hyperbolic.

Question 7

Write hyperbolic identities for these trig identities.

Answer 7

Question 8

Write double angle hyperbolic identities for these trig identities.

Answer 8

Question 9

Answer 9

Question 10

Differentiate y=sinhx

Answer 10

Question 11

Differentiate y=coshx

Answer 11

Question 12

Differentiate y=cosh3x

Answer 12

Question 13

Differentiate y=sinhxcoshx

Answer 13

Question 14

Differentiate

Answer 14

Question 15

Differentiate y=tanhx

Answer 15

Question 16

Answer 16

Question 17

Answer 17

Question 18

Integrate sinh5x .dx

Answer 18

Question 19

Integrate xcosh2x. dx

Answer 19

Question 20

Answer 20

Question 21

Answer 21

Question 22

Answer 22

Question 23

Answer 23

Question 24

Hyperbolic inverse of y=sinhx

Log form of y=arsinhx

Answer 24

Question 25

Solve coshx=4

Answer 25

Question 26

Hyperbolic inverse of y=coshx
Log form of y=arcoshx

Answer 26

Question 27

Hyperbolic inverse y=tanhx
Log form of y=artanhx

Answer 27

Question 28

Solve sinhx=6

Answer 28

Question 29

Solve tanhx=1/2

Answer 29

Question 30

Solve coshx=10

Answer 30

Question 31

Differentiate y=arsinhx

Answer 31

Question 32

Differentiate y=arcoshx

Answer 32

Question 33

Differentiate y=artanhx

Answer 33

Question 34

Sketch y=arsinhx

Answer 34

Question 35

Sketch y=arcoshx

Answer 35

Question 36

Answer 36

Question 37

Answer 37