Trigonometric equations with sin and cot

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SUMMARY

The discussion focuses on solving the trigonometric equation cot(2sin^(-1)(2/7)). Participants utilized the unit circle and the Pythagorean theorem to derive sine and cosine values. One contributor calculated the x value as 4√3, while another corrected it to 3√5. The confusion arose from interpreting the multiplication of 2 with sine in the equation, indicating a need for clarity on handling such expressions in trigonometric contexts.

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  • Understanding of trigonometric functions, specifically sine and cotangent.
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  • Knowledge of the Pythagorean theorem and its use in finding side lengths in right triangles.
  • Ability to manipulate inverse trigonometric functions, such as sin^(-1).
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  • Study the properties of cotangent and its relationship with sine and cosine.
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Homework Statement


find the value(s): cot(2sin^(-1) 2/7)

The Attempt at a Solution



I solved for sine by drawing a unit circle and the angle. I used the given values of 2 for the y value and 7 for the r value(hypotenuse). By using the pythagorean theorem I found the x value which, for me, came out to 4 sqrt(3). From the x value I was able to find the cosine. Since cotangeant is cosine/ sine I solved for that to get my exact value but it did not come out to the correct answer.
I think it had something to do with the (2 sin) in the equation. I am not sure exactly what to do when an equation gives me a number times sine.
 
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\frac{1}{tan(\frac{2}{sin(2/7)})} ?
 
dbg11 said:

Homework Statement


find the value(s): cot(2sin^(-1) 2/7)

The Attempt at a Solution



I solved for sine by drawing a unit circle and the angle. I used the given values of 2 for the y value and 7 for the r value(hypotenuse). By using the pythagorean theorem I found the x value which, for me, came out to 4 sqrt(3).
I get 3√5, not 4√3.
dbg11 said:
From the x value I was able to find the cosine. Since cotangeant is cosine/ sine I solved for that to get my exact value but it did not come out to the correct answer.
I think it had something to do with the (2 sin) in the equation. I am not sure exactly what to do when an equation gives me a number times sine.
 

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