If sin p= 3/5 and p is an acute angle, what is the value of tan p
As usual in these type of problems, construct a right-angled triangle.
sin p = opposite/hypotenuse = 3/5
You should recognize the famous 3-4-5 right-angled triangle, so the x value (the adjacent) is 4 , or else use x^2 + 3^2 = 5^2 ----> x = 4
since tan p = opposite/adjacent
tan p = 4/5
tan p = sin p / cos p
cos p = ± √ ( 1 - sin² p )
Acute angles measure less than 90°
These angles lie in the first quadrant where all trigonometric functions are positive, so:
cos p = √ ( 1 - sin² p )
cos p = √ [ 1 - ( 3 / 5 )² ] = √ ( 1 - 9 / 25 ) =
√ ( 25 / 25 - 9 / 25 ) = √ ( 16 / 25 ) = 4 / 5
tan p = sin p / cos p = ( 3 / 5 ) / ( 4 / 5 ) = 3 / 4