Math

Answer 1 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) $...

Answer 1 LetAnswer 2 Let us find the values of $cos(θ)$ and $sin(θ)$ at $θ = frac{π}{6}$:$ cosleft(frac{π}{6} ight) = frac{sqrt{3}}{2} $$ sinleft(frac{π}{6} ight) = frac{1}{2} $Answer 3 Let us find the values of $cos(θ)$ and $sin(θ)$ at $θ =...

Answer 1 To find the value of $ \tan(\frac{7\pi}{6}) $ using the unit circle:1. Locate the angle $\frac{7\pi}{6}$ on the unit circle. This angle is in the third quadrant.2. The reference angle for $\frac{7\pi}{6}$ is $\frac{\pi}{6}$.3. In the third...

Answer 1 To find the trigonometric functions of $45^\circ$ using the unit circle, note that $45^\circ$ corresponds to an angle in the first quadrant where both the x and y coordinates are equal.Since the radius of the unit circle is 1, the...

Answer 1 To find the values of $ \sin $, $ \cos $, and $ \tan $ for $ 45^{\circ} $ using the unit circle, we start with: \n \n $ \sin(45^{\circ}) = \frac{\sqrt{2}}{2} $\n $ \cos(45^{\circ}) = \frac{\sqrt{2}}{2} $\n $ \tan(45^{\circ}) = 1 $\n Answer 2...

Answer 1 To determine the cosine of the angle corresponding to the point $ \left( \frac{1}{2}, \frac{\sqrt{3}}{2} \right) $ on the unit circle, we must recognize the coordinates $(x, y)$ represent $(\cos(\theta), \sin(\theta))$.In this case, the...