SOLUTION: The point (-6, -8) is on the terminal arm of an angle 𝜽 in standard position. What is the correct ratio for sin𝜽, cos𝜽, tan𝜽?

Algebra ->  Trigonometry-basics -> SOLUTION: The point (-6, -8) is on the terminal arm of an angle 𝜽 in standard position. What is the correct ratio for sin𝜽, cos𝜽, tan𝜽?      Log On


   

Question 1159156: The point (-6, -8) is on the terminal arm of an angle 𝜽 in standard position.
What is the correct ratio for sin𝜽, cos𝜽, tan𝜽?
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
The point (-6, -8)-> angle theta is in quadrant+III
draw the triangle in that quad, the hypotenuse would be
hypotenuse=sqrt%28%28-6%29%5E2%2B%28-8%29%5E2%29=sqrt%2836%2B64%29=sqrt%28100%29=10
Note in this case theta+=+180+%2B+reference-angle%28alpha%29
sin%28alpha%29=-8%2F10=-4%2F5->-53.13°
cos%28alpha%29=-6%2F10=-3%2F5->126.9°
+tan%28alpha%29=-8%2F-6=4%2F3->53.13°
Note:
+-sin+%28alpha%29+=+sin%28+theta%29
+-cos%28+alpha+%29=+cos+%28theta%29+
+tan%28+alpha%29+=+tan+%28theta%29
that is, the sin and cos are negative in the third quadrant and the tan is positive
+tan%28+alpha%29=53.13°, then
theta+=+180+%2B+53.13=233.13° is angle in quadrant+III