find the exact value of the following.
a) cos (3pi/4)
b) cot (5 pi/3)
c) tan (13 pi/4)
please help/explain, thanks
2007-09-14 13:45:58 · 2 answers · asked by rickyricardoiscool 1 in Science & Mathematics ➔ Mathematics
unit circle, reference triangle.
a) at 3π/4, you have a 45-45-90 in quadrant 2, so cos is -√2 / 2.
b) 5π/3 , the /3 tells you 60° angles, picture the lower half circle divided into 3 parts, reference triangle in 4th quadrant, y side is -√3 / 2, x side is 1/2, tangent is -√3, so cot is -1/√3 = -√3 / 3
c) 13π/4 is coterminal with 5π/4, so 45° down into quadrant 3, tan is -1.
2007-09-14 13:56:09 · answer #1 · answered by Philo 7 · 0⤊ 0⤋
To the answerer above me,
tan(13 pi/4) = 1 since tan(x) is positive in the third quadrant.
You can also verify this by the fact that the period of tan(x) is pi.
tan (13 pi/4)
= tan(3pi + pi/4)
= tan(pi/4)
= 1
2007-09-14 21:00:58 · answer #2 · answered by sahsjing 7 · 0⤊ 0⤋