How to turn a sine function into a cosine function? if possible could someone provide an example with steps? !

Several ways may be used to turn a sine function into a cosine function, using the fundamental properties of both trigonometric functions. Here I deal with two of them.

One way is using the property cos(x) = sin (90° - x). Other is using the identity sin² (x) + cos² (x) = 1.

You will find a detailed explanation and an example below.

Step-by-step explanation:

By the definition of the sine and cosine functions, sin (90° - x) = cos (x), and cos (90° - x) = sin (x).

Hence, starting with the basic function y = sin (x), you can convert it into a cosine function substituting sin(x) with cos (90 - x), obtaining:

y = cos (90 - x)

f(x) = 3 sin (30° - 2x) = 3 cos [90° - (30° - 2x) ] = 3 cos [90° - 30° + 2x] =

      = 3 cos [60° + 2x ]

Also, you can use the fundamental identity: sin² (x) + cos² (x) = 1

From which: sin² (x) = 1 - cos²(x) ⇒ sin (x) = +/- √ [1 - cos² (x) ]

option a.

step-by-step explanation:

if you look closely at the graph, we can notice that the function is not defined at two different points.

if you look at functions b and c, you will notice that both functions are not defined at just one point. the function b is not defined at x= -5/2 and function c is not defined at x=-5. both options are discarded, given that our function should not be defined at two fiferent points.

now, if you look closely at the graph you will notice that the function sketched is not defined at x=5 and x=-2.

x =±sqrt(1/3)

step-by-step explanation:

x+4/6x=1/x

multiply each side by 6x to get rid of the fractions

6x*(x+4/6x)=1/x*6x

distribute

6x^2 +4 = 6

subtract 4 from each side

6x^2 +4-4 = 6-4

6x^2 =2

divide by 6

6x^2/6 = 2/6

x^2 = 1/3

take the square root of each side

sqrt(x^2) = ±sqrt(1/3)

x =±sqrt(1/3)