by zhanhongyuan | Feb 1, 2025 | Unit Circle
Home Find the values of $ sin( heta) $, $ cos( heta) $, and $ an( heta) $ at $ heta = frac{pi}{4} $ on the unit circle. Answer 1 Thomas Walker To find the values of $ sin(theta) $, $ cos(theta) $, and $ tan(theta) $ at $ theta = frac{pi}{4} $ on the unit circle, we...
by zhanhongyuan | Feb 1, 2025 | Unit Circle
Home Determine the sine and cosine of an angle $ heta $ in the unit circle in the second quadrant Answer 1 Charlotte Davis An angle $ theta $ in the second quadrant of the unit circle ranges from $ 90^circ $ to $ 180^circ $ (or $ frac{pi}{2} $ to $ pi $ radians). In...
by zhanhongyuan | Feb 1, 2025 | Unit Circle
Home Determine the coordinates and angles for points on the unit circle where the $cos( heta) = frac{1}{2}$. Answer 1 Alex Thompson To determine the coordinates where $cos(theta) = frac{1}{2}$ on the unit circle, we need to find $theta$ such that:$ cos(theta) =...
by zhanhongyuan | Feb 1, 2025 | Unit Circle
Home Find the angle in radians where the coordinates on the unit circle are $ left(frac{sqrt{3}}{2}, frac{1}{2}right) $ Answer 1 William King The coordinates $ left(frac{sqrt{3}}{2}, frac{1}{2}right) $ on the unit circle correspond to the angle $ frac{pi}{6} $...
by zhanhongyuan | Feb 1, 2025 | Unit Circle
Home Find the value of the integral of $ cot(x) $ from $ 0 $ to $ frac{pi}{4} $ using the unit circle. Answer 1 Ava Martin To find the value of the integral of $ cot(x) $ from $ 0 $ to $ frac{pi}{4} $ using the unit circle, we first express cotangent in terms of sine...
by zhanhongyuan | Feb 1, 2025 | Unit Circle
Home Find the value of $ sec(frac{pi}{4}) $ Answer 1 Alex Thompson To find the value of $ sec(frac{pi}{4}) $, we first find the value of $ cos(frac{pi}{4}) $. The cosine of $ frac{pi}{4} $ is $ frac{sqrt{2}}{2} $. Recall that $ sec(x) = frac{1}{cos(x)} $, so:$...
by zhanhongyuan | Feb 1, 2025 | Unit Circle
Home Calculate tangent values on the unit circle for specific angles Answer 1 Thomas Walker To calculate the tangent values for specific angles on the unit circle, you will use the formula: $ an( heta) = frac{sin( heta)}{cos( heta)} $Consider the angles $ heta =...
by zhanhongyuan | Jan 27, 2025 | Science
Home What are the differences between the planets in the inner solar system and those in the outer solar system? Answer 1 James Cain The inner planets (Mercury, Venus, Earth, Mars) are rocky, smaller, and have fewer moons. They are closer to the Sun and have shorter...
by zhanhongyuan | Jan 27, 2025 | Math
Home How do you determine the convergence or divergence of an infinite series using the Ratio Answer 1 Rhonda Johnson To determine the convergence or divergence of an infinite series using the Ratio Test, compute the limit L = lim (n→∞) |a_(n+1) / a_n|. If L < 1, the...
by zhanhongyuan | Jan 27, 2025 | Science
Home What are the mechanisms that drive the movement of tectonic plates and how do they contribute to geological phenomena such as earthquakes and mountain formation? Answer 1 Courtney Walsh The movement of tectonic plates is driven by mechanisms such as mantle...