# Start Searching the Answers

The Internet has many places to ask questions about anything imaginable and find past answers on almost everything.

The Question & Answer (Q&A) Knowledge Managenet

The Internet has many places to ask questions about anything imaginable and find past answers on almost everything.

Table of Contents

Key Equations

Sum Formula for Cosine | cos(α+β)=cosαcosβ−sinαsinβ |
---|---|

Sum Formula for Sine | sin(α+β)=sinαcosβ+cosαsinβ |

Difference Formula for Sine | sin(α−β)=sinαcosβ−cosαsinβ |

Sum Formula for Tangent | tan(α+β)=tanα+tanβ1−tanαtanβ |

Difference Formula for Tangent | cos(α−β)=cosαcosβ+sinαsinβ |

Sine of an angle is the side of the triangle that does not touch the angle divided by the hypotenuse. cosecant is the reciprical of the sin function or 1/sin(x) so that csc(x)*sin(x) = 1 when it is defined. The two can be confused since arcsin(x) is often denoted as sin^-1(x) and x^-1 is 1/x.

In a right angled triangle, the cosecant of an angle is: The length of the hypotenuse divided by the length of the side opposite the angle. The abbreviation is csc. csc θ = hypotenuse / opposite.

The unit circle definition is tan(theta)=y/x or tan(theta)=sin(theta)/cos(theta). The tangent function is negative whenever sine or cosine, but not both, are negative: the second and fourth quadrants. Tangent is also equal to the slope of the terminal side.

The ACOS function returns the inverse cosine of a number. The function is the inverse of COS and expects input in the range from -1 to 1. Get the inverse cosine of a value, in radians.

The inverse trigonometric functions sin−1(x) , cos−1(x) , and tan−1(x) , are used to find the unknown measure of an angle of a right triangle when two side lengths are known.

While arccosine and cosine do cancel out, there’s still the problem of domain. Arccos(x) itself is only defined within that domain of [-1,1]. That means you can’t plug in anything less than -1 or greater than 1 and get an answer out. Cos(arccos(x)) is a composite function.

The arccos function is the inverse of the cosine function. It returns the angle whose cosine is a given number. Means: The angle whose cosine is 0.866 is 30 degrees. Use arccos when you know the cosine of an angle and want to know the actual angle.

The difference lies in the fact that in cos 1 angle is in radian and in cos 1 degree, angle is one degree. 360 degrees is 2pi radian, so one degree= 2pi/360 radians i.e 0.01745 radians. So it is where the difference arises. So if you are not writing degree then it will be considered in radians.