Question
If sin p=3/5 and p is an acute angle what's the value of tan p
Answers
Bosnian
tan p = sin p / cos p
cos p = ± √ ( 1 - sin² p )
Acute angles measure less than 90° and all trigonometric functions of acute angle are positive so:
cos p = √ ( 1 - sin² p )
cos p = √ [ 1 - ( 3 / 5 )² ] = √ ( 1 - 9 / 25 ) =
√ ( 25 / 25 - 9 / 25 ) = √ ( 16 / 25 ) = √16 / √25
cos p = 4 / 5
Since:
tan p = sin p / cos p
tan p = ( 3 / 5 ) / ( 4 / 5 ) = 3 / 4
cos p = ± √ ( 1 - sin² p )
Acute angles measure less than 90° and all trigonometric functions of acute angle are positive so:
cos p = √ ( 1 - sin² p )
cos p = √ [ 1 - ( 3 / 5 )² ] = √ ( 1 - 9 / 25 ) =
√ ( 25 / 25 - 9 / 25 ) = √ ( 16 / 25 ) = √16 / √25
cos p = 4 / 5
Since:
tan p = sin p / cos p
tan p = ( 3 / 5 ) / ( 4 / 5 ) = 3 / 4
mathhelper
or
since sin p=3/5 and p is acute
construct a right angled triangle, and recognize the 3-4-5 right-angled
triangle, for this one: x=4, y=3, and r = 5
so tan p = 3/4
since sin p=3/5 and p is acute
construct a right angled triangle, and recognize the 3-4-5 right-angled
triangle, for this one: x=4, y=3, and r = 5
so tan p = 3/4
oobleck
Draw the right triangle involved
You have a 3-4-5 triangle
so if sin p = 3/5, then tan p = 3/4
You have a 3-4-5 triangle
so if sin p = 3/5, then tan p = 3/4