Question
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\( \theta = \sin ^ { - 1 } ( \frac { ( 1.361 ) \operatorname { Sen } 18 } { 1.33 } ) \)

Ask by Clark Vega. in Mexico
Mar 09,2025

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Answer

\[ \theta \approx 18.46^\circ \]

Solution

1. Primero, se tiene la expresión \[ \theta = \sin^{-1}\left(\frac{1.361 \cdot \sin 18^\circ}{1.33}\right) \] 2. Calculamos \( \sin 18^\circ \). Aproximadamente, \[ \sin 18^\circ \approx 0.3090 \] 3. Multiplicamos: \[ 1.361 \cdot \sin 18^\circ \approx 1.361 \cdot 0.3090 \approx 0.4208 \] 4. Dividimos el resultado entre 1.33: \[ \frac{0.4208}{1.33} \approx 0.3166 \] 5. Ahora, se halla el ángulo cuyo seno es 0.3166: \[ \theta = \sin^{-1}(0.3166) \] 6. Utilizando una calculadora (en grados), se obtiene: \[ \theta \approx 18.46^\circ \] Por lo tanto, \[ \theta \approx 18.46^\circ \]

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The Deep Dive

Did you know that the inverse sine function, or arcsine, is often used in various fields such as physics and engineering? It's super handy for calculating angles when you have the length of sides in right-angled triangles. So, if you're solving for an angle using the value of sine, you can easily find the angle using \( \theta = \sin^{-1}(x) \). Just make sure your calculator is set to the correct mode (degrees or radians) depending on your needs! Also, be careful with the domain of the arcsine function! The input must be between -1 and 1; otherwise, you might run into a bit of trouble trying to solve your equation. In your case, ensure that \(\frac { ( 1.361 ) \operatorname { Sen } 18 } { 1.33 }\) falls within this range. If it exceeds these values, you'll have to re-evaluate your calculations or parameters!

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