Solve the given trigonometry problem

  • #1
chwala
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Homework Statement
##7 \sinh x + 3 \cosh x = 9##
Relevant Equations
hyperbolic trig. equations
My question is on the highlighted part (circled in red);

Why is it wrong to pre-multiply each term by ##e^x##? to realize ,

##5e^{2x} -2-9e^x=0## as opposed to factorising by ##e^{-x} ## ?

The other steps to required solution ##x=\ln 2## is quite clear and straightforward to me.



1716546593601.png
 
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  • #2
What makes you think you cannot?
 
  • #3
...because of this next step:

1716547615185.png


I think i get it now...to find the solution for ##x##, we can solve it as i had indicated but for the integration bit; we have to make use of all the transforms...
 
Last edited:
  • #4
That solves an entirely different question than the one you asked. The one you asked about asked for the solutions of a particular equality. What that thing is is integrating 1 divided by one of the sides of the equality.
 
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FAQ: Solve the given trigonometry problem

What is the Pythagorean identity in trigonometry?

The Pythagorean identity states that for any angle θ, the following relationship holds: sin²(θ) + cos²(θ) = 1. This identity is derived from the Pythagorean theorem and is fundamental in trigonometry.

How do you solve a right triangle using trigonometric ratios?

To solve a right triangle, you can use the trigonometric ratios: sine (sin), cosine (cos), and tangent (tan). For a given angle θ, sin(θ) = opposite/hypotenuse, cos(θ) = adjacent/hypotenuse, and tan(θ) = opposite/adjacent. By knowing one angle and one side, you can find the other sides and angles using these ratios.

What are the steps to solve a trigonometric equation?

To solve a trigonometric equation, follow these steps: 1) Isolate the trigonometric function on one side of the equation. 2) Use known identities to simplify the equation if necessary. 3) Solve for the angle using inverse trigonometric functions. 4) Consider the periodic nature of trigonometric functions to find all possible solutions within the desired interval.

How do you find the exact value of trigonometric functions for special angles?

The exact values of trigonometric functions for special angles (0°, 30°, 45°, 60°, 90°, etc.) can be determined using the unit circle or special triangles. For example, sin(30°) = 1/2, cos(45°) = √2/2, and tan(60°) = √3. Memorizing these values can simplify calculations in trigonometry.

What is the difference between radians and degrees in trigonometry?

Radians and degrees are two units for measuring angles. A full circle is 360 degrees, which is equivalent to 2π radians. To convert degrees to radians, use the formula: radians = degrees × (π/180). Conversely, to convert radians to degrees, use: degrees = radians × (180/π). Radians are often preferred in calculus and higher-level mathematics due to their natural relationship with the unit circle.

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