Answer 1 To find the sine, cosine, and tangent of the angle $\frac{\pi}{4}$ on the unit circle, we need to locate the angle on the circle. The angle $\frac{\pi}{4}$ radians is equivalent to 45 degrees. In the unit circle, this corresponds to the...

Answer 1 To find $\csc(\frac{\pi}{3})$, we first need to recall the definition of the cosecant function: $\csc(\theta) = \frac{1}{\sin(\theta)}$ Next, we locate the angle $\frac{\pi}{3}$ on the unit circle. The sine of $\frac{\pi}{3}$ is given by:...

Answer 1 To find the tangent of an angle θ on the unit circle, we use the definition of tangent in terms of sine and cosine: $\tan(\theta) = \frac{\sin(\theta)}{\cos(\theta)}$ Consider the angle θ = 45 degrees. The coordinates on the unit circle are...

Answer 1 The angle $\frac{\pi}{6}$ radians corresponds to 30 degrees. On the unit circle, the coordinates of the point at this angle represent the cosine and sine values. Therefore, for the angle $\frac{\pi}{6}$: $\cos\left(\frac{\pi}{6}\right) =...

Answer 1 The formula to convert degrees to radians is: \( \theta = \frac{\pi}{180} \times \text{degrees} \)Given an angle of 120 degrees, we use the following calculation:$ \theta = \frac{\pi}{180} \times 120 $This simplifies to:$ \theta =...