4x+y=0, x≥0
help finding Sin, Cos, Tan for this
You mean for the slope of that line?
y = -4x
slope = -4
in quadrant 2
x = -1
y = 4
hypotenuse = sqrt(17)
sin = 4/sqrt17
cos = -1/sqrt17
tan =-4
in quadrant 4
x = 1
y=-4
h = sqrt 17 again
sin = -4/sqrt17
cos = 1/sqrt17
tan = -4 again
2.0308
To find the values of sine, cosine, and tangent for the given equation, we need to find the values of x and y. Let's solve the equation and find the values of x and y.
Given: 4x + y = 0 and x ≥ 0
Step 1: Solve for y in terms of x
Since 4x + y = 0, we can isolate y by subtracting 4x from both sides of the equation:
y = -4x
Step 2: Determine the value of x
Since x ≥ 0, we can choose any non-negative value for x. For simplicity, let's set x = 1.
Step 3: Plug the value of x into the equation to find y
y = -4 * 1
y = -4
Step 4: Find the values of sine, cosine, and tangent
To find the values of sine, cosine, and tangent, we need to find the values of the sides of a right triangle. Since x = 1 and y = -4, we can construct a right triangle with the sides:
Opposite side (y) = -4
Adjacent side (x) = 1
Hypotenuse = √(x^2 + y^2) = √(1^2 + (-4)^2) = √(1 + 16) = √17
Now we can find the values:
Sine (sin) = Opposite / Hypotenuse = -4 / √17
Cosine (cos) = Adjacent / Hypotenuse = 1 / √17
Tangent (tan) = Opposite / Adjacent = -4 / 1 = -4
Therefore, the values for sine, cosine, and tangent for the given equation 4x + y = 0, with x ≥ 0, are:
sin = -4 / √17
cos = 1 / √17
tan = -4
To find the sin, cos, and tan values for a given equation, we need to find the values of x and y. Let's solve the given equation to find these values.
Given equation: 4x + y = 0
Since x ≥ 0, we know that x is a non-negative value. Let's solve for y in terms of x:
4x + y = 0
Subtract 4x from both sides:
y = -4x
Now, we have the equation in terms of x and y.
To find sin, cos, and tan, we need to know the values of x and y. However, the equation alone does not provide enough information to calculate these trigonometric values.
The sin, cos, and tan functions are utilized in trigonometry, which deals with the relationships between angles in triangles. Without an angle or additional information, we cannot directly calculate these trigonometric values.
If you have any additional information related to angles or triangles, please provide it so that we can assist you further.