Trigonometry

Trigonometry is used in CSI in calculating bullet or other projectile trajectories, ballistics, analyzing what actually happened in automobile collisions, how objects fall from heights, and in many many other ways.

The inverse of the inverse is the original function, so that the product of the two functions is equivalent to the identity function on the appropriate domain.

The domain of a function is the range of the inverse function.

The range of a function is the domain of the inverse function.

It too will have a value of 5

tan 40o ~= 0.8391

An airplane flying at an altitude of 2600m, approaching an airport runaway located 48km away, is descending at an angle of 3.1 degrees, rounded to the nearest tenth of a degree.

Construct a right triangle. Horizontal is 48. Verticle (opposite) is 2.6. Hypoteneuse is 48.07 by pythagorean theorem. The inverse sine of (2.6 / 48.07) is 3.1 degrees.

For a normal school protractor it is 1 degree.

First find the circumference of the whole circle using Pi x diameter. Halve the answer and add the diameter.

Thus: 3.1416 × 10 = 31.416 ÷ 2 + 10 = 25.708cm

So the perimeter of the semi-circle is 25.7cm

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logx = 0.25 =1/4 4logx = 1 log x^4 = 1 x^4 = 10 x = 4th root of 10 =1.778

The cosine is ±1/sqrt(5) = ±0.4472 (approx).

sin 10° = 0.17364817766693 Source: http://calculator3.sdsu.edu/calculator3.php

It is 10/18 = 0.55... radians.

The sine of 75 degrees is about 0.9659

The tangent of an angle theta is defined as sine(theta) divided by cosine(theta). Since the sine and cosine are Y and X on the unit circle, then tangent(theta) is Y divided by X.

The tangent of a function at a point is the line going through that point which has slope equal to the first deriviative of the function at that point.

Sec(2x) = 1/Cos(2x)

In trigonometry, the value of R is the radius of the circle, and is usually normalized to a value of 1. If the circle is at the X-Y origin, and theta is the angle between the radius line R, and X and Y are the X and Y coordinates of the point on the circle at the radius line, then... sine(theta) = Y / R cosine(theta) = X / R secant(theta) = 1 / cosine(theta) = R / X cosecant(theta) = 1 / sine(theta) = R / Y

Confusing?

Note: When doing trigonometry, it is highly recommeded that you have a scientific calculator at hand. Also, make sure your calculator is in Degree (D or Deg) mode and not Radian (R or Rad).

To find the cosine of 70o, press 'cos', then type in 70, then press equals. You should get 0.342 (to the nearest 3 decimal places).

60

You cannot.

A right angled isosceles triangle will always be 90-45-45 so knowing the angles does not add any information. Without knowledge of any one side, you cannot distinguish between the infinitely many similar 90-45-45 triangles.

First, find the ratio of fencepost-height : shadow which is 1.6 : 2.6 . This can also be written as a fraction, 1.6/2.6 . Then, multiply the flagpole's shadow by this ratio:

31.2 x 1.6/2.6 = 19.2

The flagpole is 19.2m high.

The trigonometry way:

On the imaginary right angled triangle formed by the fencepost and its shadow, let the angle at which the hypotenuse meets the ground = θ

sinθ = 1.6/2.6

sinθ = /31.2

x/31.2 = 1.6/2.6

2.6x = 31.2 * 1.6 = 49.92

x = 19.2

The flagpole is 19.2m high.

It is 0.2048*PI radians, approx.

If, at any time, a vertical line intersects the graph of a relationship (or mapping) more than once, the relationship is not a function. (It is a one-to-many mapping and so cannot be a function.)

Theta is just a Greek letter used to denote measurement of angle. Sine is a trigonometric function, i.e., the ratio of the side opposite to the angle theta to the hypotenuse of the triangle. So Sine theta means the value of sine function for angle theta, where theta is any angle.