Trigonometry

Ancient Egyptian and Babylonian mathematicians lacked the concept of an angle measure, but they studied the ratios of the sides of similar triangles and discovered some properties of these ratios. The ancient Nubians used a similar methodology.

It has many purposes for exmaple building, architecture, astronomy and engineering.

Reciprocal of Cosine is Secant

The amplitude of a sine (or cosine) curve is the difference between the maximum and minimum values of the curve, measured over a whole cycle.

Artem Analyticam

According to the stories surrounding its development, yes.

That sounds like a triangular prism.

A number that makes an equation true is its solution.

Positive x negative = negative

(Negative x positive = negative)

Positive x positive = positive

Negative x negative = positive

So if the signs are the same the answer is positive and if they are different it is negative.

The origin or (0,0).

It is a semi-circular arc joining two diametrically opposite points on the sphere. These may be the "North" and "South" poles.

If you have the option to take Pre-Calc Algebra, do that.

Amongst the lay public of non-mathematicians and non-scientists, trigonometry is known chiefly for its application to measurement problems, yet is also often used in ways that are far more subtle, such as its place in the theory of music; still other uses are more technical, such as in number theory. The mathematical topics of Fourier series and Fourier transforms rely heavily on knowledge of trigonometric functions and find application in a number of areas, including statistics.

If the room is rectangular, multiply the the lengths of the walls. If the shape is not rectangular, you will need to break it up into rectangles or squares. Draw it out on paper and break it up into smaller parts whose area you can find.

All others can be derived from these and a little calculus:

sin2x+cos2x=1

sec2x-tan2x=1

sin(a+b)=sin(a)cos(b)+sin(b)sin(a)

cos(a+b)=cos(a)cos(b)-sin(a)sin(b)

eix=cos(x)+i*sin(x)

c^2

Trigonometric identities are trigonometric equations that are always true.

Try and show this as well as you can:

Think of a wheel, or whatever that is cylinder-shaped. One point on the wheel's base is our aim of attention. If you look at the wheel from the side, and roll it at a constant speed, one point on the wheel makes a sine curve.

You could illustrate by adding something that leaves a trail to a cylinder. Like gluing a piece of chalk on a scroll of tape. Then roll the scroll next to a blackboard, and the result should be a sine curve, where the amplitude is the same as the radius of the scroll.

The longest side of the right angles triangle is called the hypotenuse. Divide the length of the side opposite the chosen angle by the length of the hypotenuse. This is the Sine of the angle.

A rectangular prism. If every edge is the same length, then it is a cube.

Transform one side into the other, or both sides into a third thing.

The length of an arc equals he angle (in radians) times the radius. Divide the length by the radius, and that gives you the ange. Measure out the angle on a protractor and draw the length of the radius at the begining and end of the angle. Then draw theportion of the circle with its center at the location ofthe angle and extending out to the radius.

SQRT(3)/4 - 1/4

You do not need to, if you have a right triangle that angle is 90* so the other 2 angles are 45* apiece.

That is actually only partially accurate. There can be a right angled triangle with sides of 2-3-5. 5 being the hypotenuse in which the triangle's angles will not be 90-45-45 but 90-33.69-56.31. To find the angles of a right triangle, you will need to know the length of the sides. With the length of all three sides, you will need to utilize sine, cosine, and tangent to find the angles.