Hyperbolic functions

Question 1

cosh, sinh, tanh - what creates 1? List all 3

Answer 1

c - s

Question 2

State in e: cosh, sinh, tanh

Answer 2

1/2 (ex + e-x)
1/2 (ex - e-x)
(ex - e-x) / (ex + e-x)

Question 3

cosh(A±B), sinh(A±B), tanh(A±B)

Answer 3

c – cAcB ± sAsB
s – sAcB ± cAsB
t – tA ± tB / 1 ± tAtB

Question 4

State in the normal functions: cosh, sinh, tanh

Answer 4

cos ix = cosh x
sin ix = i sinh x
tan ix = i tanh x

Question 5

graph cosh, sinh, tanh, sinh-1, cosh-1, tanh-1

Answer 5

c - (0, 1) close to ex
s - gradient 1 at 0, pass origin
t - limits at |y|=1, pass origin

s - long s, no limits
c - long c, no real value where cosh x < 1
t - limits at |x|=1

Question 6

Rewrite sinh-1, cosh-1, tanh-1

Answer 6

s - ln(x + √x2+1)
c - ±ln(x ± √x2-1)
t - 1/2 ln(1+x / 1-x)

Question 7

Draw ellipse
Write equation and key parts of graph
Write in terms of trigo functions

Answer 7

A = πab
(x/a)² + (y/b)² = 1
x = a cos θ + x0
y = b sin θ + y0

Question 8

Draw hyperbola
When does it face each way
key identifiers

Answer 8

(x/a)² - (y/b)² = 1
x = ± r cosh θ )(, y no ±

y = ± r sinh θ U
if x² > 0 )(

y = bx/a

Question 9

Write circle in trigo

Answer 9

x0 + rcos
y0 + rsin

Question 10

Find roots z if cos z = 2

Answer 10

cos(x+iy) = cosx cosh y - i sin x sinh y
real -> 2
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