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Answer 1 To find the value of $ \cos(\theta) $ using the unit circle when $ \theta = \frac{5\pi}{4} $, we first locate this angle on the unit circle.The angle $ \theta = \frac{5\pi}{4} $ lies in the third quadrant.We know that $ \theta =...
Answer 1 To find the equation of the tangent line to the unit circle at $(1, 0)$, we first recognize that the unit circle has the equation:$ x^2 + y^2 = 1 $The slope of the tangent line at any point $(x_0, y_0)$ on the circle can be found using...
Answer 1 Given that $ \theta $ is an angle on the unit circle, we know that:$ \sec(\theta) = \frac{1}{\cos(\theta)} $The cosine of $ \theta $ can be found using the coordinates (x, y) of the corresponding point on the unit circle, where x represents...
Answer 1 To find the sine and cosine values for the angle $ \frac{5\pi}{4} $ using the unit circle, first note that this angle is in the third quadrant. In the unit circle, the reference angle for $ \frac{5\pi}{4} $ is $ \frac{\pi}{4} $. The sine and...
Answer 1 The unit circle has a radius of 1 and can be represented by the equation:$ x^2 + y^2 = 1 $At an angle of $\frac{3\pi}{4}$ radians, the coordinates can be determined using the sine and cosine functions:$ x = \cos\left(\frac{3\pi}{4}\right) =...
Answer 1 To evaluate the sine and cosine of $ \frac{\pi}{4} $, we use the unit circle values:The sine of $ \frac{\pi}{4} $ is:$ \sin \left( \frac{\pi}{4} \right) = \frac{\sqrt{2}}{2} $The cosine of $ \frac{\pi}{4} $ is:$ \cos \left( \frac{\pi}{4}...