SOLUTION: Find the exact values of sin θ, cos θ, and tan θ if the terminal arm of ∠θ in standard position contains the given point. P(-8, 15)

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Question 1204867: Find the exact values of sin θ, cos θ, and tan θ if the terminal arm of ∠θ in standard position contains the given point.
P(-8, 15)
Found 2 solutions by ikleyn, mananth:
Answer by ikleyn(52867) About Me  (Show Source):
You can put this solution on YOUR website!
.
Find the exact values of sin θ, cos θ, and tan θ if the terminal arm of ∠θ in standard position contains the given point.
P(-8, 15)
~~~~~~~~~~~~~~~~~ 

Point P is in QII, 2-nd quarter.

Its x-coordinate is -8.

Its y-coordinate is 15.

Its distance from the origin is  r = sqrt%28x%5E2%2By%5E2%29 = sqrt%28%28-8%29%5E2%2B15%5E2%29 = sqrt%28289%29 = 17.


sin%28theta%29 = y%2Fr = 15%2F17 = 0.88235  (rounded).


cos%28theta%29 = x%2Fr = %28-8%29%2F17 = -8%2F17 = -0.47059  (rounded).


tan%28theta%29 = y%2Fx = 15%2F%28-8%29 = -15%2F8 = -17%2F8 = -1.875  (exact value).

Solved, with complete explanations (without excessive words).

For sin%28theta%29 and cos%28theta%29 you have exact values (fractions)
and decimal expressions, that are rounded (approximate) values.



Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
Find the exact values of sin θ, cos θ, and tan θ if the terminal arm of ∠θ in standard position contains the given point.
P(-8, 15)
Calculate the hypotenuse using Pythagorean Theorem
hypotenuse=sqrt%28%28%28-8%29%5E2%2B15%5E2%29%29=sqrt%28%2864%2B225%29%29=sqrt%28289%29=17
Use the trig. definitions to find all of the angles:
sinθ=opposite/hypotenuse=15/17
cosθ=adjacent/hypotenuse= -8/17
tanθ=opposite/adjacent=-15/8
You round it off as required when you write in decimals
.