Question
Express the trig ratios as fractions in simplest terms.
W
X
Y
24
51
45
Answer
Attempt 1 out of 2
The number of attempts on this specific problem before you are marked incorrect
sin YY =
cos XX =
sin YY and cos XX
.
Submit Answer
W
X
Y
24
51
45
Answer
Attempt 1 out of 2
The number of attempts on this specific problem before you are marked incorrect
sin YY =
cos XX =
sin YY and cos XX
.
Submit Answer
Answers
Answer
are they equal or unequal
Answered by
GPT-4o mini
To express the trigonometric ratios \(\sin Y\) and \(\cos X\) as fractions in simplest terms, we first need to identify the relationships based on the values given.
From the information provided, we can assume \(Y = 24^\circ\) and \(X = 51^\circ\). However, it's not clear what the "W" represents, so we'll focus on calculating \(\sin Y\) and \(\cos X\) based on \(Y\) and \(X\) alone.
To find these values:
1. **Calculate \(\sin Y\) from angle \(Y\):**
\[
\sin(24^\circ) \text{ can be computed using a calculator or sine table.}
\]
Approximating, we find:
\[
\sin(24^\circ) \approx 0.4067
\]
2. **Calculate \(\cos X\) from angle \(X\):**
\[
\cos(51^\circ) \text{ can also be computed using a calculator or cosine table.}
\]
Approximating, we find:
\[
\cos(51^\circ) \approx 0.6293
\]
Since the problem asks for the simplest fraction, we can express the values rounded to a recognizable form, often these values are left in decimal form for practical problems without known fractions directly equivalent.
If you need the radians or specific fraction simplification, you may need to provide right triangles or convert angles into known special angles, assuming \(Y\) and \(X\) are labeled for triangles.
For the sake of simplifying, let's provide approximate fractional equivalents, based on known values:
- An approximate fraction for \(\sin Y\) is \( \frac{4067}{10000} \), which does not reduce nicely.
- An approximate fraction for \(\cos X\) is \( \frac{6293}{10000} \), also which does not reduce nicely.
If the request is strict about simplifying to known radians or special ratios, please clarify further or provide context on any right triangle that these angles might be related to.
In conclusion:
- \(\sin Y \approx 0.4067\) or approximated fractionally as \(\frac{4067}{10000}\)
- \(\cos X \approx 0.6293\) or approximated fractionally as \(\frac{6293}{10000}\)
If these values need to be submitted or further simplified, please ensure calculations are run through correct calculator functions.
Submit as required based on these entries.
From the information provided, we can assume \(Y = 24^\circ\) and \(X = 51^\circ\). However, it's not clear what the "W" represents, so we'll focus on calculating \(\sin Y\) and \(\cos X\) based on \(Y\) and \(X\) alone.
To find these values:
1. **Calculate \(\sin Y\) from angle \(Y\):**
\[
\sin(24^\circ) \text{ can be computed using a calculator or sine table.}
\]
Approximating, we find:
\[
\sin(24^\circ) \approx 0.4067
\]
2. **Calculate \(\cos X\) from angle \(X\):**
\[
\cos(51^\circ) \text{ can also be computed using a calculator or cosine table.}
\]
Approximating, we find:
\[
\cos(51^\circ) \approx 0.6293
\]
Since the problem asks for the simplest fraction, we can express the values rounded to a recognizable form, often these values are left in decimal form for practical problems without known fractions directly equivalent.
If you need the radians or specific fraction simplification, you may need to provide right triangles or convert angles into known special angles, assuming \(Y\) and \(X\) are labeled for triangles.
For the sake of simplifying, let's provide approximate fractional equivalents, based on known values:
- An approximate fraction for \(\sin Y\) is \( \frac{4067}{10000} \), which does not reduce nicely.
- An approximate fraction for \(\cos X\) is \( \frac{6293}{10000} \), also which does not reduce nicely.
If the request is strict about simplifying to known radians or special ratios, please clarify further or provide context on any right triangle that these angles might be related to.
In conclusion:
- \(\sin Y \approx 0.4067\) or approximated fractionally as \(\frac{4067}{10000}\)
- \(\cos X \approx 0.6293\) or approximated fractionally as \(\frac{6293}{10000}\)
If these values need to be submitted or further simplified, please ensure calculations are run through correct calculator functions.
Submit as required based on these entries.
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