For what x is tan x 1

Trigonometry introduction

The following introduction covers angles and trigonometric functions. There are 6 basic trigonometric functions that are most easily explained using a right triangle. There is an unknown angle in this triangle xas in the drawing shown.

The basic functions use the length of the hypotenuse (the longest side), the opposite cathede, the angle x facing, and the adjacent (Adjacent), which at the angle x is applied.

The sine of x, written sin (x), is defined as:

sin (x)=Opposite cathete
Hypotenuse

The cosine of x, written cos (x), is defined as:

 

The tangent of x, written tan (x), is defined as:

tan (x)=Opposite cathetus
Affiliate

Note that tan (x) is undefined at the point x = 0.

Knowing an angle and the length of one side of a right triangle makes it very easy to find the second side.

For angles between 90 and 180 degrees:
    sin (x) == sin (180 - x)
cos (x) == - cos (180 - x)
tan (x) == - tan (180 - x)

For angles between 0 to 90 degrees:
sin (x) == -sin (x)
cos (x) == cos (x)
tan (x) == -tan (x)

For angles between 180 and 270 degrees:
    sin (x) == - sin (180 + x)
cos (x) == cos (180 + x)
tan (x) == - tan (180 + x)
For angles between 270 and 360 degrees:
    sin (x) == - sin (360-x)
cos (x) == - cos (360-x)
tan (x) == tan (360-x)

Sin-1(x) or asin (x) denotes the inverse sine function or arc sine. This indicates the angle whose sine is x. Similar to arc cosine and arc tangent. A quick look at the table above shows that there can be different answers for an arc function. This is why physical formulas with arc functions usually require the range in which the angle may lie.

Remarks:

C-Script provides trigonometric functions for var-Variables unsupported by lite-C for var (in Pure mode) and for double. The var-Functions use angles in. For compatibility reasons with Gamestudio Degree (0 ... 360), their counterparts, double, however, use angles in Radians (0 ... 2 pi) to be compatible with C. So always be clear about which angle you want to use!

Some useful functions:

tan (x) = sin (x) / cos (x)
sin2(x) + cos2(x) = 1
sin (x + y) = sin (x) cos (y) + cos (x) sin (y)

sin (x-y) = sin (x) cos (y) - cos (x) sin (y)

cos (x + y) = cos (x) cos (y) - sin (x) sin (y)

cos (x-y) = cos (x) cos (y) + sin (x) sin (y)

tan (x + y) = (tan (x) + tan (y)) / (1 - tan (x) tan (y))

tan (x-y) = (tan (x) - tan (y)) / (1 + tan (x) tan (y))

By using the above formulas x = y replace, we get:

sin (2x) = 2 sin (x) cos (x)

cos (2x) = cos2(x) - sin2(x)

tan (2x) = 2 tan (x) / (1 - tan2(x))