Final answer:
Using the given value of sin(B) = 4/13 and the formulas for cosec, cos, tan, sec, and cot, the exact values of the remaining trig functions for angle B are:
1) cosec(B) = 13/4
2) cos(B) = ±√(3/13)
3) tan(B) = (4√3)/3
4) sec(B) = (√39)/3
5) cot(B) = (√3)/4
Step-by-step explanation:
To find the exact values of the remaining trig functions for angle B, given that sin(B) = 4/13, we can use the following formulas:
cosec(B) = 1/sin(B)
cos(B) = ±√(1 - sin^2(B))
tan(B) = sin(B)/cos(B)
sec(B) = 1/cos(B)
cot(B) = 1/tan(B)
Let's substitute the given value of sin(B) = 4/13 into these formulas:
1) cosec(B) = 1/(4/13)
= 13/4
2) cos(B) = ±√(1 - (4/13)^2)
= ±√(1 - 16/169)
= ±√(153/169)
= ±√(3/13)
3) tan(B) = (4/13)/(±√(3/13))
= 4/√3
= (4√3)/3
4) sec(B) = 1/(±√(3/13))
= √(13/3)
= (√13)/√3
= (√39)/3
5) cot(B) = 1/tan(B)
= 3/(4√3)
= (√3)/4