SOLUTION: 1. Find the values of the remaining functions if tan=1/4, sin<0 sin= cos= csc= sec= cot= 2. Find the values of the remaining functions if cos=3/5 in quadrant IV. sin= tan=

Algebra ->  Trigonometry-basics -> SOLUTION: 1. Find the values of the remaining functions if tan=1/4, sin<0 sin= cos= csc= sec= cot= 2. Find the values of the remaining functions if cos=3/5 in quadrant IV. sin= tan=       Log On


   



Question 1072971: 1. Find the values of the remaining functions if tan=1/4, sin<0
sin=
cos=
csc=
sec=
cot=
2. Find the values of the remaining functions if cos=3/5 in quadrant IV.
sin=
tan=
csc=
sec=
cot=
3. Graph y=tan [2(x-pi/4)]
Period=
Phase Shift=
Vertical Shift=
4. Graph y=-2 sec (x-pi/2)
Period=
Phase Shift=
Vertical Shift=
Amplitude=
Very confused on these homework problems, any help is appreciated!

Found 2 solutions by MaxWong, MathTherapy:
Answer by MaxWong(38) About Me  (Show Source):
You can put this solution on YOUR website!
1. tan x = 1/4
Consider a 1 - 4 - sqrt(17) right angle triangle
Therefore
sin x = 1/sqrt(17)
cos x = 4/sqrt(17)
tan x = 1/4
csc x = sqrt(17)
sec x = sqrt(17)/4
cot x = 4

Answer by MathTherapy(10553) About Me  (Show Source):
You can put this solution on YOUR website!
1. Find the values of the remaining functions if tan=1/4, sin<0
sin=
cos=
csc=
sec=
cot=
2. Find the values of the remaining functions if cos=3/5 in quadrant IV.
sin=
tan=
csc=
sec=
cot=
3. Graph y=tan [2(x-pi/4)]
Period=
Phase Shift=
Vertical Shift=
4. Graph y=-2 sec (x-pi/2)
Period=
Phase Shift=
Vertical Shift=
Amplitude=
Very confused on these homework problems, any help is appreciated!
You can't post so many problems simultaneously!
I'll help you with # 1.
As matrix%281%2C3%2C+tan+%28theta%29%2C+%22=%22%2C+1%2F4%29, and matrix%281%2C3%2C+sin+%28theta%29%2C+%22%3C%22%2C+0%29, it's obvious that theta is in the 3rd quadrant
matrix%281%2C5%2C+tan+%28theta%29%2C+%22=%22%2C+%28-+1%29%2F%28-+4%29%2C+%22=%22%2C+y%2Fx%29
y%5E2+%2B+x%5E2+=+r%5E2
%28-+1%29%5E2+%2B+%28-+4%29%5E2+=+r%5E2
17+=+r%5E2
matrix%281%2C3%2C+r%2C+%22=%22%2C+sqrt%2817%29%29


highlight_green%28matrix%281%2C3%2C+csc+%28theta%29%2C+%22=%22%2C+-+sqrt%2817%29%29%29
highlight_green%28matrix%281%2C3%2C+sec+%28theta%29%2C+%22=%22%2C+-+sqrt%2817%29%2F4%29%29
highlight_green%28matrix%281%2C3%2C+cot+%28theta%29%2C+%22=%22%2C+4%29%29