Find the exact values of $sin(x)$ and $cos(x)$ for all solutions in the third quadrant for the equation $2sin(x) + 3cos(x) = 1$
Answer 1
William King
To find the exact values of $\sin(x)$ and $\cos(x)$ for all solutions in the third quadrant for the equation $2\sin(x) + 3\cos(x) = 1$, consider the trigonometric identity:
$ \sin^2(x) + \cos^2(x) = 1 $
In the third quadrant, both $ \sin(x) $ and $ \cos(x) $ are negative. Let
Answer 2
Amelia Mitchell
Given the equation $2sin(x) + 3cos(x) = 1$, we need to find the exact values of $sin(x)$ and $cos(x)$ in the third quadrant. Consider:
$ sin^2(x) + cos^2(x) = 1 $
In the third quadrant, both $ sin(x) $ and $ cos(x) $ are negative. Set $ sin(x) = -a $ and $ cos(x) = -b $:
$ 2(-a) + 3(-b) = 1 $
Which simplifies to:
$ -2a – 3b = 1 $
We also have:
$ a^2 + b^2 = 1 $
Solving for $a$ and $b$ will give the exact values of $sin(x)$ and $cos(x)$.
Answer 3
Emma Johnson
For the equation $2sin(x) + 3cos(x) = 1$ in the third quadrant, set $sin(x) = -a$ and $cos(x) = -b$:
$ -2a – 3b = 1 $
With:
$ a^2 + b^2 = 1 $
Solve for $a$ and $b$ to get $sin(x)$ and $cos(x)$.
Start Using PopAi Today