Trigonometry

The famous mathematical problems featuring pi include finding the area and the circumference of a circle. The value for pi is 3.14.

• 56, 126,
• 40, 110,
• and 77, 147.

Mystery message

The powers of i are:

i1 = i

i2 = -1

i1 = -i

i1 = 1

After that, the pattern repeats, so i6 = -1.

Descriptive is when a few represent the whole population. Inferential infer the nature of a lager usually infinite set of data that we don't have.

The slope of a line tells a person what the rate of change is for a certain amount of time. For instance, on a graph where distance is the X axis and time is the Y axis, the slope will tell the velocity, literally, distance/time.

It depends on your latitude. At the equator (0 degrees) a degree of longitude covers just over 111 km, so 8 degrees would be about 890 km.

At 45 degrees of latitude, a degree of longitude covers just under 79 km, so 8 degress would be about 555 km.

Check out the calculator in the related link. Enter the degrees of latitude and it gives the length of a degree at that point.

Suppose the cube has edges of length x.

Then the area of each face (side) is x2. There are six faces so the total surface area is 6x2. The volume of the cube is x3.

So 6x2 = x3

DIviding both sides by x2 gives x = 6.

This would be pi/4 radians or 45 degrees.

65°

sine(sin) = opp/hypcosecant(q) = hyp/oppcosine(cos) = adj/hypsecant(q) = hyp/adjtangent(tan) = opp/adjcotangent(q) = adj/opp

The period is 1 millisecond.

sin(70 deg) = 0.9397 approx.

it can be written as follows

nf=m+a=R

Where n stands for needs, f for faith,m for motivation, a for action and R represents result.

sin(3x) = 3sin(x) - 4sin^3(x)

You can use the inverse of sin when you want to solve an equation where x is the angle you're trying to find.

Say sin(x)=32/50

Since you can't plug "x" into your calculator, use the arc sin (represented on your calculator by sin -1) on both sides to get rid of the sin. This is how it would plug into your calculator:

sin-1 (32/50)

Whatever the answer is would be what "x" equals.

Use the tangent ratio:

tan = 22.5/34 = 45/68

tan-1(45/68) = 33.49518467 degrees

Angle of elevation = 33o29'42.66''

Approx 2.6131

y=sin x

y=cos x cos x

sin x = cos^2 x

sin x = 1-sin^2 x

sin x -1 + sin^2 x = 0

sin^2 x + sin x -1 = 0

Let y=sin x

y^2+y-1 = 0

This equation is of form ay^2+by+c=0

a = 1 b = 1 c = -1

y=[-b+/-sqrt(b^2-4ac)]/2a]

y=[-1 +/-sqrt(1^2-4(1)(-1)]/(2)(1)

discriminant is b^2-4ac =5

y=[-1 +√(5)] / 2

y=[-1 -√(5)] / 2

sin x = [-1 +√(5)] / 2

x = sin^-1 [-1 +√(5)] / 2] = 0.6662394 radians

x = sin^-1 [-1 -√(5)] / 2] = sin^-1 (-1.618) -- has no solution

When x = 0.6662394 radians, sin x and cos x times cos x are equal.

Leaving aside the fuzziness caused by atmospheric diffraction the curve (called the Terminator!) is really a straight line running North-South. North and South in this context are "poles" perpendicular to the plane of the earth's orbit around the sun and should not be confused with the geographic or magnetic N and S.

Unfortunately for map makers, the earth is approximately spherical and so they need to use some form of projection to represent the earth on a 2-dimensional (flat) surface. This process distorts the geography of the earth. For example, the most commonly used projection, the Mercator projection, greatly exaggerates the size of the polar regions with this exaggeration reducing as one moves towards the equator. Other projections introduce other distortions. Since the earth's axis is tilted, the NS for the Terminator are different from the geographic NS and as a result the terminator appears as a curve. Its exact shape is determined by the projection used even though in reality it is a straight line.

I assume. Since theta is a variable, standing for the measure of any angle.

Simple harmonic motion (SHM( is defined by the second order differential equation:

d2y/dt2 = -ky

where y is a fubction of time, t and is the displacement (relative to the central position), and k is a positive constant.

The equation says is that at any given position of the object undergoing SHM, its acceleration is proportional to its displacement from, and directed towards the central position.

The sine and cosine functions are solutions to the differential equation.

The tangent of 0.47 radians is about 0.508. The tangent of 0.47 degrees is about 0.00820.

Secant is 1 over cosine and cosine 0 equals 1.

By converting everything to sines and cosines. Since tan x = sin x / cos x, in the cotangent, which is the reciprocal of the tangent: cot x = cos x / sin x. You can replace any other variable (like thetha) for the angle.