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Answer 1 Using the unit circle, we can find the values of $\sin(\frac{\pi}{4})$ and $\cos(\frac{\pi}{4})$ by locating the angle $\frac{\pi}{4}$ radians. This angle corresponds to a 45-degree angle in the unit circle.At this angle, both the...
Answer 1 To find the cosine of $45^\circ$, we use the unit circle. On the unit circle, the coordinates of the point where the terminal side of the $45^\circ$ angle intersects the circle are $(\frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2})$. The cosine of an...
Answer 1 Let's determine the sine, cosine, and tangent values for the angle θ = 225° on the unit circle.First, convert the angle to radians: $ θ = 225° = \frac{225π}{180} = \frac{5π}{4} radians $Using the properties of the unit circle, we know: $...
Answer 1 Consider a unit circle with center at the origin (0,0). Let the endpoints of the chord be at coordinates (cos θ, sin θ) and (cos φ, sin φ). The formula for finding the distance between two points (x1, y1) and (x2, y2) is given by:$ d =...
Answer 1 Let's consider an angle $ \theta $ in the unit circle. The coordinates of a point on the unit circle are given by $(\cos \theta, \sin \theta)$. The tangent of the angle $ \theta $ is defined as:$\tan \theta = \frac{\sin \theta}{\cos...
Answer 1 Given a point on the unit circle, say $(\cos(\theta), \sin(\theta))$, we need to find the tangent line at this point.Step 1: The equation of the unit circle is $x^2 + y^2 = 1$.Step 2: To find the slope of the tangent, we differentiate...