Trigonometry

Arthur Pythagoras rules! 12 x 12 = 3 x 3 + x2, so x2 = 144 - 9 and x = sqrt 135 = 11.62 so to the nearest foot it reaches 12 feet (actually 11.62)

-1<cosine<1

Sine and cosine are cofunctions, which means that their angles are complementary. Consequently, sin (90° - x) = cos x. Secant is the reciprocal of cosine so that sec x = 1/(cos x). Knowing these properties of trigonometric functions, among others, will really help you in other advance math courses.

10 sin71 = 10 x 0.9455 = 9.455 feet (just under 9' 5½")

The sine of 22.5 degrees is 0.383

Cosine(42 radians) = -0.399985

Cosine(42 degrees) = 0.743146

0 degree to 90 degrees.

It is -sqrt(1 + cot^2 theta)

90 degrees

x = (2n+1)*pi/2 radians for any integer n.

22227 feet

This is a right triangle with an angle equal to 13 degrees, and the side opposite that angle equal to 5000 ft (6000-1000). We need to find the hypotenuse (which we will call x) of the triangle (i.e., the length of the trail). Because sin(theta)=opposite side/hypotenuse.

Therefore we have:

sin(13 deg)=5000/x

Solving for x:

x=5000/sin(13 deg)=22227

[Be sure that you are using degrees rather than radians; otherwise, you will get a wrong answer. If your calculator is using radians and you don't want to change it, you first need to convert 13 degrees to radians by multiplying 13 by (pi/180).] Using radians, you would do the same as above, but the last line would be:

x=5000/sin(13*pi/180)=22227

SOHCAHTOA
This would be the sine, the opposite over the hypotenuse.
5000/h=sin 30 degrees
5000 divided by sin 30 degrees= trail

No more than means the number or less.

For example, no more than five could be 1, 2, 3, 4, or 5 but no higher. It couldn't be 6, 7 or 8 etc.

that's right, but to added on -1, -2, -3, -4, or -5 can be too.

Loads and loads of formulas.

That's trigonometry. ;-)

y = -1 + 3 sin 4x

Let's look at the equation of y = 3 sin 4x, which is of the form y = A sin Bx, where

the amplitude = |A|, and the period = (2pi)/B.

So that the amplitude of the graph of y = 3 sin 4x is |3| = 3, which tell us that the maximum value of y is 3 and the minimum value is -3, and the period is (2pi)/4 = pi/2, which tell us that each cycle is completed in pi/2 radians.

The graph of y = -1 + 3 sin 4x has the same amplitude and period as y = 3 sin 4x, and translates the graph of y = 3 sin 4x one unit down, so that the maximum value of y becomes 2 and the minimum value becomes -4.

Sin theta of 30 degrees is

1/2

that purely depends on the given polygon and any information about it

4

They are the projections, onto the x and y [Cartesian] axes, of a point whose polar coordinates are (R, theta).

It's a common Trig way to express a point when a radius is rotated around a given angle. For example, where exactly would the edge of a two foot gate lie if the gate opened 30 degrees? R is two feet. Two times cosine 30 is the x coordinate and two times sine 30 is the y coordinate.

at a 45 degree angle, or pi/4

The area is 99.0 square units.

Provided that any denominator is non-zero,

sin = sqrt(1 - cos^2)tan = sqrt(1 - cos^2)/cos

sec = 1/cos

cosec = 1/sqrt(1 - cos^2)

cot = cos/sqrt(1 - cos^2)

If cos B is 5/13, find sin B, tan B, sec B, and cot B?

sin= y/r= 12/13
cos= x/r= 5/13
tan= y/x= 12/5
csc= r/y= 13/12
sec= r/x= 13/5
cot= x/y= 5/12

x2+y2=r2

cot[x]= -1

cot[x] = cos[x] / sin[x]

cos[x] / sin[x] = -1

cos[x] = -sin[x]

|cos[x]| = |sin[x]| at every multiple of Pi/4 + Pi/2. However, the signs disagree at 3Pi/4 + nPi, where n is an integer.

To find the sine ratio of a right-angled triangle divide the opposite by the hypotenuse.

For example: 4/5 = 0.8 units and sine-1(0.8) = 53.13010235 degrees.