If the given point is on the terminal arm of an angle A in stadard position. 0 degrees more than or equal too A and less than or equal too 180 degree, find sin A and cos A:
a) (6,8) b) (-5,12)
Can you tell me how you get it because I do not understand it at all please help!
answered
look at your previous post
To find sin A and cos A for a given point on the terminal arm of angle A in standard position, we can use the Pythagorean Theorem and the definitions of sine and cosine.
Let's first consider point (6,8). The coordinates of this point give us the lengths of the two sides of a right triangle formed by the x-axis, y-axis, and the terminal arm of angle A. The horizontal side of the triangle has length 6 and the vertical side has length 8.
Using the Pythagorean Theorem, we can find the length of the hypotenuse (the side opposite angle A):
c^2 = a^2 + b^2
c^2 = 6^2 + 8^2
c^2 = 36 + 64
c^2 = 100
c = 10
Now that we know the length of the hypotenuse, we can calculate sin A and cos A:
sin A = opposite/hypotenuse = 8/10 = 0.8
cos A = adjacent/hypotenuse = 6/10 = 0.6
Therefore, for point (6,8), sin A is approximately 0.8 and cos A is approximately 0.6.
Now let's move on to point (-5,12). As before, the coordinates give us the lengths of the horizontal and vertical sides of the right triangle. The horizontal side has length -5 (negative since it's to the left of the origin) and the vertical side has length 12.
Using the Pythagorean Theorem:
c^2 = (-5)^2 + 12^2
c^2 = 25 + 144
c^2 = 169
c = 13
Now we can calculate sin A and cos A:
sin A = 12/13 ≈ 0.923
cos A = -5/13 ≈ -0.385
Therefore, for point (-5,12), sin A is approximately 0.923 and cos A is approximately -0.385.