if point P is a point on the terminal side of 0, and 0 is in standard position, find sin 0,cos 0 and tan 0.
1. P(-6,8) 2. P (1,3) 3. P (-2,-40), 4. P (-5, -12)
Something missing here.
I need the coordinates of point P
To find the values of sin θ, cos θ, and tan θ for the given points, we can use the distance formula and trigonometric ratios. Let's go step by step for each point:
1. P(-6,8):
First, let's find the distance from the origin (0,0) to the point P(-6, 8). We can use the distance formula:
d = √[(x₂ - x₁)² + (y₂ - y₁)²]
d = √[(-6 - 0)² + (8 - 0)²]
d = √[36 + 64]
d = √100
d = 10
Now, we can find the values of sin θ, cos θ, and tan θ using the following formulas:
sin θ = y / r
cos θ = x / r
tan θ = y / x
sin θ = 8 / 10
cos θ = -6 / 10
tan θ = 8 / -6
So, for point P(-6,8), sin θ = 0.8, cos θ = -0.6, and tan θ = -1.33.
2. P(1,3):
Using the same process as before, we find the distance from the origin to P(1, 3):
d = √[(1 - 0)² + (3 - 0)²]
d = √[1 + 9]
d = √10
Now let's find sin θ, cos θ, and tan θ:
sin θ = 3 / √10
cos θ = 1 / √10
tan θ = 3 / 1
So, for point P(1,3), sin θ = 0.95, cos θ = 0.32, and tan θ = 3.
3. P(-2,-40):
Calculating the distance from the origin to P(-2,-40):
d = √[(0 - -2)² + (0 - -40)²]
d = √[4 + 1600]
d = √1604
Finding sin θ, cos θ, and tan θ:
sin θ = -40 / √1604
cos θ = -2 / √1604
tan θ = -40 / -2
So, for point P(-2,-40), sin θ = -0.998, cos θ = -0.0619, and tan θ = 20.
4. P(-5, -12):
Finding the distance from the origin to P(-5,-12):
d = √[(-5 - 0)² + (-12 - 0)²]
d = √[25 + 144]
d = √169
d = 13
Now let's determine sin θ, cos θ, and tan θ:
sin θ = -12 / 13
cos θ = -5 / 13
tan θ = -12 / -5
So, for point P(-5,-12), sin θ = -0.923, cos θ = -0.385, and tan θ = 2.4.
These are the values of sin θ, cos θ, and tan θ for each given point.