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The angle for which the sine value is 0.6691 is found to be 42°.
What is the sine value?
A trigonometric function called sin x, where x is the angle under discussion stands for the sine of an angle. The sine function is the proportion between the perpendicular and hypotenuse of a right-angled triangle. In other words, the hypotenuse and its value change as the angle changes, and it is the ratio of the side opposite to the angle under discussion. In the study of physics, sound and light waves are represented by the sine function.
When the angle between a right-angled triangle's base and hypotenuse changes, the sine's value changes.
=41.99°≈42°
Learn more about sine values here:
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<h3>Answer:</h3>
(5, -2, -3)
<h3>Explanation:</h3>We assume your equations are ...
- x +3y -z = 2
- 4x +2y +5z = 1
- 3x +0y +z = 12
These have solution (x, y, z) = (5, -2, -3).
_____
<em>How we know</em>
Trying the choices in the last equation eliminates the first and last. Trying the second choice in the first equation eliminates it, leaving the 3rd choice as the answer you're looking for.
We also know because we can ask a graphing calculator to solve the matrix equation (or row-reduce the augmented matrix).
<em>Comment on this problem</em>
The hardest part of this problem is figuring your intent. The equations are not well-separated, so we have a hard time telling what is a constant and what is a coefficient. It took a couple of guesses to sort it out. A little editing before posting would be helpful.