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Answer 1 To find the $\tan$ values of the unit circle at specific angles, we can use the fact that $\tan(\theta) = \frac{\sin(\theta)}{\cos(\theta)}$: 1. At $\theta = \frac{\pi}{4}$, $ \tan(\frac{\pi}{4}) =...
Answer 1 To find the coordinates on the unit circle for the angle $\frac{7\pi}{6}$, we use the unit circle properties: The unit circle coordinates $(x, y)$ for an angle $\theta$ are $(\cos(\theta), \sin(\theta))$. For $\theta = \frac{7\pi}{6}$: $ x =...
Answer 1 To find the values of $\sin(\theta)$, $\cos(\theta)$, and $\tan(\theta)$ for $\theta = \frac{\pi}{4}$ using the unit circle, we use the following: On the unit circle, at $\theta = \frac{\pi}{4}$, the coordinates are: $(\frac{1}{\sqrt{2}},...
Answer 1 To find the values of $ \sin(\theta) $ at specific angles on the unit circle, we can use the known values for common angles:At $ \theta = 0 $, $ \sin(0) = 0 $At $ \theta = \frac{\pi}{2} $, $ \sin\left(\frac{\pi}{2}\right) = 1 $At $ \theta =...
Answer 1 We start with the definitions of the trigonometric functions on the unit circle.\n $ \tan(\theta) = \frac{\sin(\theta)}{\cos(\theta)} $\n $ \sec(\theta) = \frac{1}{\cos(\theta)} $\n Multiplying these two expressions, we have:\n $...
Answer 1 The unit circle is defined by the equation: $ x^2 + y^2 = 1 $ The positive x-axis means $ y = 0 $. Substituting $ y = 0 $ into the equation gives: $ x^2 + 0^2 = 1 $ Simplifying, we find: $ x^2 = 1 $ Taking the positive square root (since we...