given tan=(3/4) and sin<0, how do you find the other 4 trigonometric functions??

Answer 1

Since sine is negative, you are in quadrant 3 or 4. Since tangent is positive, this narrows you down to quadrant 3. Draw a triangle from the origin into quad. 3. The angle formed between the x-axis and the hypotenuse you just drew is A. Since tan A = 3/4, label the vertical side -3 and the horizontal side -4. Then the hypotenuse must be 5 (common Pythagorean triple).

So cos A = -4/5
sin A = -3/5
tan A = 3/4

The other 3 are just reciprocals:
sec A = -5/4
csc A = -5/3
cot A = 4/3

Answer 2

Tan x = 3/4 means hypotenuse = 5 [3-4-5 rt triangle]
cot x = 4/3
sin x = 3/5
cscx = 5/3
cos x = 4/5
sec x = 5/4
The above is true int he 1st quadrant
It is also true for sin and csc in 2nd quadrant,
for the tan and cot in the 3rd quadrant, and
for the cos and sec in the 4th quadrant

Answer 3

secx = 4 = 4/a million = hyp/adj adjacent area = a million hypotenuse = 4 a^ + b^2 = c^2 --> b^2 = c^2 - a^2 b^2 = (4)^2 - (a million)^2 b^2 = 15 b = opposite area = ?15 sinx = opp/hyp = ?15/4 cscx = a million/sinx = 4/?15 tanx = opp/adj = ?15/a million = ?15 cotx = a million/tanx = a million/?15

Answer 4

O/H
A/H
O/A