SOLUTION: Each point lies on the terminal arm of an angle. Determine the six trigonometric ratios for the angle, rounded to four decimal places. a) A(5, 12) b) B(4, 3) d) D(7, 24)

Algebra ->  Trigonometry-basics -> SOLUTION: Each point lies on the terminal arm of an angle. Determine the six trigonometric ratios for the angle, rounded to four decimal places. a) A(5, 12) b) B(4, 3) d) D(7, 24)       Log On


   

Question 1161054: Each point lies on the terminal arm of an angle. Determine the six trigonometric ratios for the angle, rounded to four decimal places.
a) A(5, 12)
b) B(4, 3)
d) D(7, 24)
Found 3 solutions by Alan3354, MathLover1, MathTherapy:
Answer by Alan3354(69443) About Me  (Show Source):
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Each point lies on the terminal arm of an angle. Determine the six trigonometric ratios for the angle, rounded to four decimal places.
a) A(5, 12)
---
r = sqrt(x^2 + y^2)
r = 13
---
sin = y/r
cos = x/r
tan = y/x
---
cot = 1/tan
sec = 1/cos
csc = 1/sin
==============================
Do the other the same way.
It is important to understand it, not just get the answer.
===============
b) B(4, 3)
d) D(7, 24)

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

Each point lies on the terminal arm of an angle. Determine the six trigonometric ratios for the angle, rounded to four decimal places.
a)
A(5, 12)
=>x=5 and y=12
find r
r%5E2=x%5E2%2By%5E2
r=sqrt%285%5E2%2B12%5E2%29
r=sqrt%2825%2B144%29
r=sqrt%28169%29
r=13
The six trigonometric functions are:
sine%28x%29+=y%2Fr=12%2F13=0.9231
cos%28x%29=x%2Fr=5%2F13=0.3846
tan%28x%29=y%2Fx=12%2F5=2.4000
cot%28x%29+=x%2Fy=5%2F12=0.4167
sec%28x%29=r%2Fx=13%2F5=2.6000
csc%28x%29+=r%2Fy=13%2F12=1.0833

b)
B(4, 3)
=>x=4 and y=3
find r
r%5E2=x%5E2%2By%5E2
r=sqrt%284%5E2%2B3%5E2%29
r=sqrt%2825%29
r=5
The six trigonometric functions are:
sine%28x%29+=y%2Fr=3%2F5=0.6000
cos%28x%29=x%2Fr=4%2F5=0.8000
tan%28x%29=y%2Fx=3%2F4=0.7500
cot%28x%29+=x%2Fy=4%2F3=1.3333
sec%28x%29=r%2Fx=5%2F4=1.2500
csc%28x%29+=r%2Fy=5%2F3=1.6667+



d)
D(7, 24)
=>x=7 and y=24
r=sqrt%287%5E2%2B24%5E2%29
r=sqrt%28625%29
r=25
The six trigonometric functions are:
sine%28x%29+=y%2Fr=24%2F25=0.9600
cos%28x%29=x%2Fr=7%2F25=0.2800
tan%28x%29=y%2Fx=24%2F7=3.4286
cot%28x%29+=x%2Fy=7%2F24=0.2917
sec%28x%29=r%2Fx=25%2F7=3.5714
csc%28x%29+=r%2Fy=25%2F24=1.0417+

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
Each point lies on the terminal arm of an angle. Determine the six trigonometric ratios for the angle, rounded to four decimal places.
a) A(5, 12)
b) B(4, 3)
d) D(7, 24)
Just 1 needs to be done, so you can follow it and do the remaining 2. 

a) (5, 12) indicates (x, y), so x = 5; y = 12

This represents a 5-12-13 PYTHAG. TRIPLE, which means that r = 13.

Trigonometric Ratios: 

Just substitute the 3 variables.

b) and d) are ALSO PYTHAGOREAN TRIPLES.

FYI: Always present TRIG. functions as exact values, unless asked to do otherwise. 

And, never, never present them as the other person did. For most of these problems, she has no clue!