Unit Circle

Answer 1 To find the trigonometric functions for the angle $ \frac{7\pi}{6} $, locate the angle on the unit circle.First, convert $ \frac{7\pi}{6} $ to degrees: $ \frac{7\pi}{6} \times \frac{180^\circ}{\pi} = 210^\circ $Next, find the reference...

Answer 1 To find the tangent value of $ \frac{\pi}{4} $ in the unit circle, use the definition of tangent:$ \tan(\theta) = \frac{\sin(\theta)}{\cos(\theta)} $At $ \theta = \frac{\pi}{4} $, both the sine and cosine values are:$ \sin(\frac{\pi}{4}) =...

Answer 1 To find where the derivative of $ \cos(\theta) $ equals zero, we first need to find the derivative: $ \frac{d}{d\theta} \cos(\theta) = -\sin(\theta) $ Set the derivative to zero: $ -\sin(\theta) = 0 $ Thus, we have: $ \sin(\theta) = 0 $ The...

Answer 1 To determine the coordinates of the points on the unit circle where the angle is $ \frac{\pi}{4} $, we need to use trigonometric functions.On the unit circle, the x-coordinate is given by $ \cos(\theta) $ and the y-coordinate is given by $...

Answer 1 To find the reference angle for $345^\circ$, note that it is in the fourth quadrant. The reference angle in the fourth quadrant is found by subtracting the given angle from $360^\circ$: $ 360^\circ - 345^\circ = 15^\circ $So, the reference...