The inverse of a cosine function is the
function

arcsine

secant

arccosine

cosecant

cosecant

Step-by-step explanation:

Inverse Cosine

cos-1

Cos-1

arccos

Arccos

The inverse function of cosine.

Basic idea: To find cos-1 (½), we ask "what angle has cosine equal to ½?" The answer is 60°. As a result we say cos-1 (½) = 60°. In radians this is cos-1 (½) = π/3.

More: There are actually many angles that have cosine equal to ½. We are really asking "what is the simplest, most basic angle that has cosine equal to ½?" As before, the answer is 60°. Thus cos-1 (½) = 60° or cos-1 (½) = π/3.

Details: What is cos-1 (–½)? Do we choose 120°, –120°, 240°, or some other angle? The answer is 120°. With inverse cosine, we select the angle on the top half of the unit circle. Thus cos-1 (–½) = 120° or cos-1 (–½) = 2π/3.

In other words, the range of cos-1 is restricted to [0, 180°] or [0, π].

Note: arccos refers to "arc cosine", or the radian measure of the arc on a circle corresponding to a given value of cosine.

Technical note: Since none of the six trig functions sine, cosine, tangent, cosecant, secant, and cotangent are one-to-one, their inverses are not functions. Each trig function can have its domain restricted, however, in order to make its inverse a function. Some mathematicians write these restricted trig functions and their inverses with an initial capital letter (e.g. Cos or Cos-1). However, most mathematicians do not follow this practice. This website does not distinguish between capitalized and uncapitalized trig functions.



See also

Inverse trigonometry, inverse trig functions, interval notation

infinitely many solutions

step-by-step explanation:

we have been given the equation;

2(2x + 3) = -4 + 2(2x + 5)

we need to determine the value of x.

2(2x + 3), we expand this expression to obtain 4x + 6

similarly 2(2x + 5) will become 4x + 10

now we have;

4x + 6 = -4 + 4x + 10

4x + 6 = 4x + 10 - 4

4x + 6 = 4x + 6

the expression on the left hand side is identical to the one on the right hand side. therefore, we are looking at just a single straight line whose equation is;

y = 4x + 6

consequently, we shall have infinitely many solutions