Search 74,244 tutors
FIND TUTORS
Ask a question

Answers by Kevin C.

Find cos2x (answer)

Use the double angle formula:  cos2x = 1 - 2sin2x.   Therefore, if sinx = -3/5, and sin2x = 9/25,   cos2x = 1 - 2(9/25) = 1 - 18/25 = 25/25 - 18/25 = 7/25.   BUT: Since the angle lies in quadrant 3, (π < x < 3π/2), the double angle, 2x lies between...

... or using de Moivre's Theorem:  wk =  z1/n = (rcisθ)1/n = r1/n (cis(θ+360k)/n), where k = 0 and 1, and n = 2, z = 0 + 2i, so r = 2, and θ = 90°.   we get w0 = √2 (cis(90/2)), and w1 = √2 (cis(90 + 360)/2);   So, w0 = √2 cos 45 + √2 i sin...

Find cos theta/2 (answer)

Hi, David.   The half angle formula:  cos(θ/2) = ±√((1 + cosθ)/2).   Since sinθ = 3/5, cosθ = 4/5.   Therefore, (1+cosθ)/2  = 9/10, and cos(θ/2) = ±√.9.   Since 0 < θ < π,  we know that 0 < θ/2 < π/2, and cos(θ/2)...

Find sin theta/2 (answer)

Hi, David.   The half angle formula:  sin(θ/2) =± √((1-cosθ)/2).   Therefore, (1-cosθ)/2 = (1+.6)/2 = .8.   sin(θ/2) = ±√(.8)   and  since π/2 < θ < 3π/2, Π/4 < θ/2 < 3π/4,  sin(θ/2) is ±√(.8).   I hope...

The arithmetic mean is the average of 2 or more numbers.   The arithmetic mean of x and y is:  (x + y)/2.   The geometric mean is the square root of the product of two numbers.   For example:  the geometric mean of 4 and 9 is 6, the square root...

y = cos-1(1/2) = π/3 and, since the cos is also positive for (3π/2, 2π), the answer needs to include 5π/3.   The value of arccos0 has two values:  at π/2, and 3π/2.   Arccos(-15/17):  x = -15, r = 17, and y = 8.  Therefore, the cot must = x/y, or -15/8.   If...

x cos y = 2 (answer)

Hi, Ehsan.   Using the product formula, taking the derivative of: x cos y = 2,   We get:  1 cos y  + x (-sin y) dy/dx = 0   So -x sin y (dy/dx) = -cos y,   Divide by -xsiny, dy/dx = (cos y)/(x sin y) = (cot y)/x.   Since...

First:  multiply all equations by 10.     5a + 3b = 22 12c + 85b = -244 33c + 13a = 290   Eliminate b from the first 2 equations, getting an equation in a and c.   Use that and the 3rd equation to solve for a and c.    Finally,...

Plane figures (answer)

Q1.  Do you mean hextagon or hexagon?  The last three are parallelograms, and therefore, by definition, are polygons with parallel sides.   Also, all hexagons don't have any parallel sides unless they are regular or they may have only 2 parallel sides.

point slope (answer)

Hi, Lisa.   Remember that the point-slope form of a linear equation with point (x1, y1) and slope m:   y - y1 = m(x - x1)  and the slope-intercept form: y = mx + b.   Therefore, using the points (-5, -10), and (-9, 8), we find the slope: (8 - (-10))/(-9...

2x2 + 1 = 6x   First, put this in standard form:  2x2 - 6x + 1 = 0   Using a = 2, b = -6, and c = 1, the quadratic formula gives: x = (6 ±√(36 - 4(2)(1)))/4   So x = (6 ± √(36 - 8)/3 = (6 ± √28)/4 = (6 ± 2√7)/4 = (3 ± √7)/2  ...

Using the formula A = P(1 + r/n)^(nt)  where P = principal, r = rate, n = number of times per year, and t = number of years.   we get A = 6300(1 + .06/2)^(2*2) = 7090.71   I hope this helps.