# 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)

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Expert Answers

thilina-g | Certified Educator

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`