The coordinates of a point P on a terminal arm of an angle A in standard position are given where A lies between 0 degree and 360 degrees. Determine the measures of sin A, cos A and tan A.
The graph below represents the point P ( black dot) on the terminal arm of an angle A in standard position.
A right angled triangle is created by drawing a vertical line from the point P to the base.
The length of the line opposite the angle in this case is 3 and the length of the line adjacent to the angle is 6. The hypotenuse has a length equal to `sqrt(3^2 + 6^2)` = `sqrt(9+36)` = `sqrt 45` = `3*sqrt 5`
The value of sin A is equal to (opposite side)/(hypotenuse) = `3/(3*sqrt 5) = 1/sqrt 5`
The value of cosine A = adjacent side/hypotenuse = `6/(3*sqrt5) = 2/sqrt 5`
The value of tan A = opposite side/adjacent side = `3/6 = 1/2`
A similar procedure can be used to find the measure of the trigonometric functions for any given angle A.