Trigonometry

There is no single law in trigonometry so the question makes no sense.

2sinx - sin3x = 0

2sinx - 3sinx + 4sin3x = 0

4sin3x - sinx = 0

sinx(4sin2x - 1) = 0

sinx*(2sinx - 1)(2sinx + 1) = 0

so sinx = 0

or sinx = -1/2

or sinx = 1/2

It is not possible to go any further since the domain for x is not defined.

For simplicity's sake, X represent theta.

This is the original problem: sin2x+ cosX = cos2X + sinX

This handy-dandy property is key for all you trig fanatics: sin2x+ cos2x = 1

With this basic property, you can figure out that

sin2 x=1-cos2x

and

cos2x= 1-sin2x

So we can change the original problem to:

1-cos2x+cosx = 1-sin2X + sinX

-cos2x + cosx =-sin2x + sinX

Basic logic tells you that one of two things are happening.

sin2x is equal to sinx AND cos2x is equal to cosx. The only two numbers that are the same squared as they are to the first power are 1 and 0. X could equal 0, which has a cosine of 1 and a sine of 0, or it could equal pi/2, which has a cosine of 0 and a sine of 1.

The other possibility whatever x (or theta) is, it's sine is equal to its cosine. This happens twice on the unit circle, once at pi/4 and once at 5pi/4.

If you're solving for all possible values for x and not just a set range on the unit circle, then the final solution is:

x=0+2pin x=pi/2+2pin x= pi/4 +2pin x=5pi/4+2pin (note that n is a variable)

Cosine of -90 is 0.

1.732

length of the slide= 47.10 feet

A unit circle is in the coordinate plane where both axes are measured in real numbers. The imaginary circle is in the complex plane in which one axis (horizontal) measures the real component of a complex number and the other axis measures the imaginary component.

0.525321989

Round the base angle to 70 degrees and use the sine ratio:

30*sine 70 degrees = 28.19077862 feet

Height of ladder from the ground = 28 feet to 2 s.f.

tan-1(0.575) = 29.8989 degrees (rounded)

cos 2x = cos2 x - sin2 x

= 2 cos2 x - 1; whence,

cos 2x / cos x = 2 cos x - (1 / cos x)

= 2 cos x - sec x.

One example I know is an ice cream cone.

Yes.

Using Pythagorean's theorem: 202+212 = 400+441 = 841 = 292 = 841

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. ;-)

I dont think it has uses in daily life..its just to find the area of a triangle

Example: Express sin 120⁰ as a function of an acute angle (an angle between 0⁰ and 90⁰).

Solution:

Each angle θ whose terminal side lies in quadrant II, III, or IV has associated with it an angle called the reference angle, alpha (alpha is formed by the x-axis and the terminal side).

Since 120⁰ lies on the second quadrant, then alpha = 180⁰ - 120⁰ = 60⁰.

Since sine is positive in the second quadrant, sin 120⁰ = sin 60⁰.


Example: Express tan 320⁰ as a function of an acute angle.

Solution:

Since 320⁰ lies on the fourth quadrant, then alpha = 360⁰ - 320⁰ = 40⁰.

Since tangent is negative in the fourth quadrant, tan 320⁰ = -tan 40⁰.

cos(-100 degrees)

1 minute of arc is one sixtieth, or about 0.01667, of a degree. The sine of of 0.01667 degrees is about 0.0002909.

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.