Question

Sin(π)+4cos(π) = x - cos(π/2)

Answer 1

To solve for x in the trigonometric equation, the known values of sine and cosine for specific angles are substituted. Upon calculation, the solution is found to be x = -4.

Step-by-step explanation:

The question given is a trigonometric equation involving standard angles. To solve for x, we use known values of sine and cosine functions at specific angles. We have:

sin(π)+4cos(π) = x - cos(π/2)

Substitute the known values:

sin(π) = 0

cos(π) = -1

cos(π/2) = 0

Now, calculate the left side of the equation:

0 + 4(-1) = 0 - 4

Then the equation becomes:

-4 = x - 0

Finally:

x = -4 + 0

x = -4

This equation showcases an antinode in a wave function and makes use of trigonometric identities, including the law of sines and law of cosines, which are fundamental in solving various problems in mathematics and physics.

Answer 2

x=-0.85840734 or x=π -4