Question
Using the Pythagorean Identity, determine cosθ if sinθ=79 and π2<θ<π .(1 point)
Answers
Answered by
GPT-4o mini
To find \( \cos \theta \) using the Pythagorean identity, we can use the formula:
\[
\sin^2 \theta + \cos^2 \theta = 1
\]
Given that \( \sin \theta = 79 \), we first need to calculate \( \sin^2 \theta \):
\[
\sin^2 \theta = 79^2 = 6241
\]
Now we can substitute into the Pythagorean identity:
\[
6241 + \cos^2 \theta = 1
\]
This simplifies to:
\[
\cos^2 \theta = 1 - 6241 = -6240
\]
Since the result is negative, we see that there is no real solution for \( \cos \theta \) given that \( \sin \theta = 79 \). The sine function can only take values in the range \([-1, 1]\). Thus, \( \sin \theta = 79 \) is not a valid value, and therefore, it is impossible to find a corresponding \( \cos \theta \) in this case.
In a standard context, such values for sine do not exist. Would you like help with a different question or concept?
\[
\sin^2 \theta + \cos^2 \theta = 1
\]
Given that \( \sin \theta = 79 \), we first need to calculate \( \sin^2 \theta \):
\[
\sin^2 \theta = 79^2 = 6241
\]
Now we can substitute into the Pythagorean identity:
\[
6241 + \cos^2 \theta = 1
\]
This simplifies to:
\[
\cos^2 \theta = 1 - 6241 = -6240
\]
Since the result is negative, we see that there is no real solution for \( \cos \theta \) given that \( \sin \theta = 79 \). The sine function can only take values in the range \([-1, 1]\). Thus, \( \sin \theta = 79 \) is not a valid value, and therefore, it is impossible to find a corresponding \( \cos \theta \) in this case.
In a standard context, such values for sine do not exist. Would you like help with a different question or concept?