Pre-Calculus

Pre-Calculus.

[Audio] As we know, a line segment has two endpoints. Now if we know the coordinates of the endpoints, then we can calculate the length of the line segment by the following distance formula. Distance = √ ( X2 -X1)2+(-Y2 –Y1))2 As such, a line segment with the coordinates (2, -3_ and ( -,1- 2), the distance of the line segment is the square root of the square of two minus negative one and the square of negative three minus negative two. The answer is approximately three point one six..

[Audio] When Calculating the midpoint of a line segment, we use the coordinates given in the midpoint formula: M=((x1+x2)/2,(y1+y2)/2) In this case, the coordinates provided are ( 2, 6) and ( 8, 12). Replacing these coordinates in the formula and dividing them by two provides ( 5, 9) as the midpoint of these segment..

[Audio] The equation of the line in slope-intercept form is given by: y = mx + c Here, (x, y) = Every point on the line m = Slope of the line Therefore, m = 3 Y = -5 and x = -2. Hence putting the value in the equation means c = - 5 + 6 = 1 meaning the equation will be y = 3x + 1. c = y-intercept of the line Usually, x and y have to be kept as the variables while using the above formula..

[Audio] In this case, the y-intercept is simply b = - 2 or (0,2) while the slope is m = . Since the slope is positive, we expect the line to be increasing when viewed from left to right. The slope is m = , that means, we go up 3 units and move to the right 4 units, then connect the two points to graph the line..

[Audio] Sin 105° can be written as sin (60° + 45°) which is similar to sin ( A + B). We know that, the formula for sin (A + B) = sin A × cos B + cos A × sin B. This means, sin 105° = sin ( 60° + 45°) = sin 60° × cos 45° + cos 60° × sin 45°. Simplified sin 105 degrees is equals to (√ 3+ 1)/2√ 2..

[Audio] When converting degrees to radians, the angle α in radians is equal to the angle α in degrees times pi constant divided by 180 degrees. This means converting 30 degrees is equals to 0.5236 radians. When converting radians to degrees, the angle α in degrees is equal to the angle α in radians times 180 degrees divided by pi constant. This means converting to radians is equals to 114.592 degrees, as seen above..

[Audio] The center angle, θ = 4 radians, radius, r = 6 inches . Using the arc length formula = θ × r = 4 × 6 = 24 inches. Arc length = 24 inches.

[Audio] When converting 45 degrees to radians: 45 = radians * ( 180 / pi) 45 = 57.32 * radians radians = 45 / 57.32 radians = 0.785 Most often, when writing degree measure in radians, pi is not calculated in, so for this problem, the more accurate answer would be: radians = 45 pi / 180 = pi / 4..