1)Which angle is coterminal with a -400 degree angle in standard postion?
A)40
B)80
C)320
D)400
I chose A
(for the next one I don't know what its called but it looks like 0 with a horizontal line through the middle.)
2)Find the exact value of cos looks like 0 with a horizontal line through the middle if the terminal side of 0 with a horizontal line through the middle in standard postion contains the point (6,-8).
A)-4/5
B)3/5
C)4/5
D)-3/5
I chose B
plus or minus all the way around or 360 changes nothing, so add 360 first
-400 + 360 = -40
well usually standard is counterclockwise from the x axis so
-40 = 360 -40 = 320
I would choose C
2,
That is called THETA but I will call it T
It is in the fourth quadrant between 270 and 360
the hypotenuse of this 3,4,5 triangle = 2*5 = 10
the cosine = adjacent/hypotenuse = +6/10==+3/5
B = agree
C for the first one. All of them aside from 320 lie in Quadrant 1. 320 and -400 lie in Quadrant 4. Since 400 is negative it moves clockwise, when the other angles move counterclockwise.
I'm not sure what you're asking in the 2nd. The exact value of cos theta with a horizontal line through the middle of the angle?
Remember a negative angle is a clockwise rotation, so a -400º angle goes all the way around and down another 40º into the fourth quadrant.
Using the standard notation that would be an angle of 320º
for your second question you are probably looking at cosθ, or cos theta.
Theta is often used as the variable to represent an angle and is one of the Greek letters.
So draw a triangle by joining the origin to the point (6,-8), which is the fourth quadrant
cosθ = adjacent/hypotenuse
hypotenuse = √(6^2 + (-8)^2) = 10
adjacent = 6
so cosθ = 6/10 = 3/5
For the first question, we need to find the angle that is coterminal with a -400 degree angle in standard position. To do this, we can add or subtract multiples of 360 degrees until we reach an angle in the range between 0 and 360 degrees.
-400 degrees + 360 degrees = -40 degrees
Therefore, an angle that is coterminal with -400 degrees is -40 degrees.
Among the given options, A) 40 degrees is the correct answer.
For the second question, we are given that the terminal side of the angle, which looks like a 0 with a horizontal line through the middle, contains the point (6, -8). We need to find the exact value of the cosine of this angle.
Since the point (6, -8) lies on the terminal side of the angle, we can use the coordinates to find the values of sin and cos.
The formula for cosine is cos(theta) = adjacent / hypotenuse.
We can determine the adjacent and hypotenuse sides of the triangle formed by the point (6, -8) as follows:
Adjacent side = x-coordinate = 6
Hypotenuse = distance from the origin to the point (6,-8) = sqrt(6^2 + (-8)^2) = sqrt(36 + 64) = sqrt(100) = 10
Now, we can plug these values into the formula:
cos(theta) = 6/10 = 3/5
Therefore, the exact value of cos(theta) is 3/5.
Among the given options, B) 3/5 is the correct answer.