Question

1. # The Terminal Side Of An Angle In Standard Position Passes Through P(–3, –4). What Is The Value Of ?

Angles are a fundamental concept in geometry, and they’re used to measure the size, shape, and direction of triangles, polygons, and other shapes. The terminal side of an angle is the line segment that extends from the origin (or vertex) of the angle to infinity. The position or orientation of an angle can generally be described in either standard or non-standard form. In standard position, an angle’s terminal side passes through a point on the Cartesian coordinate plane. For example, if you have an angle in standard position whose terminal side passes through P(–3, –4), what would be its value? Read on to find out!

## The Terminal Side Of An Angle

The terminal side of an angle in standard position passes through P(–, –). The value of can be positive or negative, depending on which quadrant the point P is in. If P is in the first or fourth quadrant, then the value of will be positive. If P is in the second or third quadrant, then the value of will be negative.

## Standard Position

An angle in standard position is an angle whose vertex is at the origin and whose initial side passes through the positive x-axis. The terminal side of an angle in standard position passes through P(–, –). The value of can be found by using the coordinates of P and the fact that the terminal side must pass through the origin.

P(-2, -5)

Since the terminal side must pass through both (-2, -5) and the origin, it must have a slope of 5/2. Therefore, = 5/2.

## Passing Through P(–3, –4)

To find the value of , we need to first calculate the coordinates of point P. We can do this by using the Pythagorean theorem. In this case, we have:

P = (−3,−4)

A = 3

B = 4

C = ?

Thus, we have: C^2 = A^2 + B^2 which means that C = sqrt(A^2 + B^2) which gives us C = 5 . So, the coordinates of point P are (5, 0). Since the terminal side of an angle in standard position passes through point P, that means that the angle itself must be 5 degrees.

## The Value Of

An angle in standard position is one whose vertex is at the origin and whose initial side passes through the positive x-axis. The terminal side of such an angle passes through the point P(x, y). The value of x can be positive or negative, but y must be positive for the terminal side to pass through P.

We can find the value of by using the fact that an angle in standard position forms a right triangle with its initial and terminal sides. Thus, we can use the Pythagorean theorem to find that . Therefore, the value of is  5 for the given point P(-3, -4).

## Conclusion

In conclusion, we have learned that the terminal side of an angle in standard position passes through P(–3, –4), and the value of is 270 degrees. We have seen how to use the slope-intercept form to identify a line equation given two points and then use trigonometric functions to find the measure of an angle. This knowledge is essential for any student studying mathematics or engineering as it provides them with a strong foundation on which they can build upon. With practice, these skills will become more natural making solving math problems easier than ever before.

2. It’s a tricky problem to solve, but if you know a few basic concepts of geometry and trigonometry, you can easily figure out the answer to this question.

Let’s start off by understanding what a “standard position” is. It’s a way of representing an angle in the coordinate plane. It’s a way to determine the angle’s direction, size, and sense (i.e., whether it is positive or negative).

In this particular case, the terminal side of an angle in standard position passes through point P(-3, -4). This means that the angle’s vertex (or starting point) is located at the origin (0, 0).

Now, to figure out the value of , we need to use trigonometry. We can use the Pythagorean theorem to calculate the length of the hypotenuse of the triangle formed by the three points (the vertex, point P, and the terminal side).

Let’s say that the hypotenuse has length c (which we will calculate in a moment). Then, the sides of the triangle have lengths a (from the vertex to point P) and b (from the vertex to the terminal side).

Using the Pythagorean theorem, we can calculate the length of the hypotenuse:

c2 = a2 + b2

c2 = (−3)2 + (−4)2 = 9 + 16 = 25

c = √25 = 5

Now, to calculate , we can use the inverse cosine function.

cos–1(b/c) = cos–1((−4)/5) = cos–1(−0.8) = 2.356194…

So, the value of in this case is 2.356194…

We hope this explanation helped you understand the answer to the question.