What is the general solution for -2sinh(t-2)=0 ?

The general solution for -2sinh(t-2)=0 is t=2

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Popular Trigonometry >

-2sinh(t-2)=0

Solution

- 2 sinh (t - 2) = 0

Solution

t = 2

Degrees

t = 114.59155 \dots^{\circ}

Solution steps

- 2 sinh (t - 2) = 0

Rewrite using trig identities

- 2 sinh (t - 2) = 0

Use the Hyperbolic identity:

sinh (x) = \frac{e ^{x} - e ^{- x}}{2}

- 2 \cdot \frac{e ^{t - 2} - e ^{- (t - 2)}}{2} = 0

- 2 \cdot \frac{e ^{t - 2} - e ^{- (t - 2)}}{2} = 0

- 2 \cdot \frac{e ^{t - 2} - e ^{- (t - 2)}}{2} = 0 : t = 2

- 2 \cdot \frac{e ^{t - 2} - e ^{- (t - 2)}}{2} = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

\frac{e ^{t - 2} - e ^{- (t - 2)}}{2} = 0

Solve

\frac{e ^{t - 2} - e ^{- (t - 2)}}{2} = 0 : t = 2

\frac{e ^{t - 2} - e ^{- (t - 2)}}{2} = 0

\frac{f ( x )}{g ( x )} = 0 \Rightarrow f (x) = 0

e^{t - 2} - e^{- (t - 2)} = 0

Add

e^{- (t - 2)}

to both sides

e^{t - 2} - e^{- (t - 2)} + e^{- (t - 2)} = 0 + e^{- (t - 2)}

Simplify

e^{t - 2} = e^{- (t - 2)}

Apply exponent rules

e^{t - 2} = e^{- (t - 2)}

a^{f (x)} = a^{g (x)}

, then

f (x) = g (x)

t - 2 = - (t - 2)

t - 2 = - (t - 2)

Solve

t - 2 = - (t - 2) : t = 2

t - 2 = - (t - 2)

Expand

- (t - 2) : - t + 2

- (t - 2)

Distribute parentheses

= - (t) - (- 2)

Apply minus-plus rules

- (- a) = a, - (a) = - a

= - t + 2

t - 2 = - t + 2

Move

2

to the right side

t - 2 = - t + 2

Add

2

to both sides

t - 2 + 2 = - t + 2 + 2

Simplify

t = - t + 4

t = - t + 4

Move

t

to the left side

t = - t + 4

Add

t

to both sides

t + t = - t + 4 + t

Simplify

2 t = 4

2 t = 4

Divide both sides by

2

2 t = 4

Divide both sides by

2

\frac{2 t}{2} = \frac{4}{2}

Simplify

t = 2

t = 2

t = 2

t = 2

t = 2

Graph

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Frequently Asked Questions (FAQ)

What is the general solution for -2sinh(t-2)=0 ?
The general solution for -2sinh(t-2)=0 is t=2