Trigonometry

tan(135) = -tan(180-135) = -tan(45) = -1

cos(t) - cos(t)*sin2(t) = cos(t)*[1 - sin2(t)]

But [1 - sin2(t)] = cos2(t)

So, the expression = cos(t)*cos2(t) = cos3(t)

In a triangle a/SinA = b/SinB = c/SinC

Since angle A = 43 and angle C is 72, angle B = (180) - (72 + 43) = 65

Hence 20/Sin65 = c/Sin72

20/0.9063 = c/0.9510

c = (20 x 0.9510)/0.9063 = 20.9864

If you are really talking about a closed triangle ABC, then the length of side "a" (given as 19) does not matter in the calculation.

Sum of the angles of a triangle is 180 degrees. Angle B and C add up to 15 + 65 = 80 degrees. Hence angle A is (180 - 80) = 100 degrees

The theorem is used for right triangles. It means the two smaller sides squared and added together equal the hypotenuse squared.

The three ways to use it will let you find the third side if you were given two other sides.

a2 + b2 = c2

b2 = c2 - a2

a2 = c2 - b2

If you mean practical ways to use it, then there are some examples:

1. Suppose you want to know how long of a ladder you need. The ladder would be the hypotenuse. The distance from the ladder to the wall at the floor is one of the shorter legs of the triangle, and the height of the wall is the other leg. So if you know how tall the wall is and how far you want the base of the ladder from the wall, then you can use the formula to calculate how long you need the ladder. Then you'd round up to the nearest available size.

2. Perhaps you need the height of a tower. You can measure from the base to a convenient viewing spot. Using surveying equipment, you can get the angle to the tip of the tower and then use trigonometry (tangent function if I remember right) to calculate the length of the hypotenuse. Then you'd subtract the distance of the base squared from the calculated length squared to get the height of the tower or other object.

3. You can calculate the distance you saved by cutting through a lot as opposed to going around the corner. You've always heard that a straight line is the shortest distance, and you can use the formula to find out how much. For instance, lets say the lot is 3 feet by 2 feet. That is five feet if you take the corner. If you cut through, you are taking the hypotenuse. So lets calculate that distance. A2 is 9 (3 x 3). B2 is 4 (2 x 2). That means C2 is 13. So C must be 3.61 (if you round up). It is nearly 1.39 feet shorter cutting across than going around.

Twenty divided by the cosine of 32 gives you 23.584 ft

The answer depends on what else you know about the shape.

The cosecant of an angle is the reciprocal of the sine of that angle. So, to find the cosecant of 105 degrees, you first need to find the sine of 105 degrees. The sine of 105 degrees is approximately 0.9659. Therefore, the cosecant of 105 degrees is approximately 1.0353 (1 divided by 0.9659).

(sqrt 2) / 2

negative one half

There are several ways to look at it....

The peak amplitude of the functions y = sin(x) and y = cos(x) is 1.

The peak-to-peak amplitude of the functions is 2.

The RMS (root mean square) amplitude of the functions is the reciprocal of the square root of two (2-½ ≈ 0.707).

360o - 215o

= 145o

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You must think of the unit circle.

negative theta is in either radians or degrees and represents a specific area on the unit circle. Remember the unit circle is also like a coordinate plane and cos is the x while sin is the y coordinate. Here is an example:

cos(-45): The cos of negative 45 degrees is pi/4 and cos(45) is also pi/4

slope intercept formula is given by y = mx+c where m is the slope and c is the x intercept

so ur equation comes to... y=(0.25)x + 24

cos(x)=sin(x-tau/4)

tan(x)=sin(x)/cos(x)

sin(x)=tan(x)*cos(x)

cos(x)=tan(x-tau/4)*cos(x-tau/4)

you can see that we have some circular reasoning going on, so the best we can do is express it as a combination of sines and cotangents:

cos(x)=1/cot(x-tau/4)*sin(x-tau/2)

tau=2*pi

They are mathematical functions.

Most people are introduced to them as trigonometric functions. In the context of a right angled triangle, with one of its angles being theta,

Cos(theta) = The ratio of the lengths of the adjacent side and the hypotenuse.

Sin(theta) = The ratio of the lengths of the opposite side and the hypotenuse.

More advanced mathematicians will know them simply as the following infinite series:

Cos(theta) = 1 - x2/2! + x4/4! - x6/6! + ...

and

Sin(theta) = x/1! - x3/3! + x5/5! - x7/7! + ...

n! = 1*2*3* ... *n

That depends on the value of the angle, theta. csc is short for "cosecans", and is the reciprocal of the sine. That is, csc theta = 1 / sin theta.

Remember that tan = sin/cos.

So your expression is sin/cos times cos.

That's sin(theta).

The sine of an angle is obtained from a right angle triangle. The other two angles are acute, or less than 90 degrees. The sin of the angle is the side opposite the angle divided by the hypotenuse.

Yes.

An equation that is not a function is called a relation. Functions are special types of relations where every input (or in other words each value in the domain) has exactly one output (or matches up with exactly one value in the range).

A relation would be where you plug in a number for x but instead of only getting one number out for y, you get more than one. Example:

y2=x

If you plug in 4 for x and solve for y by taking the square root, then y could equal either positive 2 or negative 2, since 22 is 4 and (-2)2 is also 4. In this case, x corresponds with two output values for y (2 and -2) which means that while this equation is a relation, it is not a function.

Domain here would refer to all numbers that make sense for x. In other words, what numbers can you plug in for x, and get an answer that is not imaginary or undefined. In the example above, I could not plug in negative numbers for x, because when I try to solve for y I would get an imaginary number. So we would say that the domain of that relation is x> or equal to 0.

The Range for a relation is all of the possible output values. So for all the values of x that you can plug in, what are all the possible values of y I could get out? If you look at it, since I'm only plugging in 0 for x or any other number larger than 0, that would imply that y can only be 0 or bigger as well. So the range here would be y > or equal to 0.

I hope that helps!

in trigo..180 degees = ∏ radians.. so 510 = 180*2+ 150 = 2∏ + 5∏/6 =17∏/6

tan(30 deg) = 0.5774, approx.

1.1519+k*pi radians or 66+180*k degrees for all integers k.

Volume = 6.86.86.8 = 314.432 cubic cm