calculate the values of sin angle, cos angle,and tan angle, if terminal arm of angle in standard position contains the point P(3,4)
The terminal arm of the angle contains the point, x=3 and y =4
Therefore we can draw a triangle restricted by the following lines,
the terminal arm of the angle, x-axis and x = 3 line.
The length of the terminal arm of that triangle can be found by the pythagorean theorem.
The pythagorean theorem says if a and b length are perpendicular in a right angled triangle, the other length c, which is facing the right angle is given by,
`c = sqrt(a^2+b^2)`
so the length of the side of the triangle facing the right angle is,
`c = sqrt(3^2+4^2) = sqrt(9+16) = sqrt(25) = 5`
Therefore from that angle you get (let's call the angle as A):
`sin(A) = 4/5 = 0.8`
`cos(A) = 3/5 = 0.6`
`tan(A) = 4/3 = 1.3333`