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)

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)   (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)
---
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)   (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(, )
=> and
find

The six trigonometric functions are:

b)
B(, )
=> and
find

The six trigonometric functions are:

d)
D(, )
=> and

The six trigonometric functions are:

Answer by MathTherapy(10553)   (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!
RELATED QUESTIONS
The point P(-4,7) lies on the terminal arm of an angle in standard position. Determine... (answered by Alan3354)
The point (-3,7) lies on the terminal arm for angle 0 . Determine the primary and... (answered by mananth)
The point A( - 3, - 5) is on the terminal arm of an angle θ. Determine exact... (answered by ewatrrr)
The point P(-4,-7) lies on the terminal arm of an angle in standard position. Determine... (answered by Alan3354)
The terminal arm of an angle, θ , in standard position passes through Q(3, 4). a)... (answered by Alan3354)
One of the primary trigonometric ratios for an angle is given, as well as the quadrant... (answered by math_helper,solver91311,MathTherapy)
For the point (sqrt2/2,sqrt2/2) on the terminal side of an angle, determine the six... (answered by Alan3354)
The point Q(− ,2 − 5) lies on the terminal arm of an angle θ in standard position.... (answered by MathLover1)
Find the (exact) value of the six trigonometric ratios associated with the angle... (answered by lwsshak3)