0

# Find the value of ALL the other five trigonometric functions, given tanx= 4/11, secx<0.

Thanks for the help! If you could please show all your work? Thanks again!

### 3 Answers by Expert Tutors

Jane B. | Master's degree in Education. Focus on success for all students.Master's degree in Education. Focus on s...
4.8 4.8 (5 lesson ratings) (5)
0
Kirill and Felice gave good answers, but I wanted to add this to eliminate any confusion.

We can only use trig functions with right triangles, so you have to use Pythagorean's Theorem to solve for the hypotenuse: a2+b2=c2. a and b = 4 and 11, in either order, according to the problem. Therefore, c2=137; c=sqrt137.

I hope that fills in any gaps. Kirill and Felice covered the rest of the explanation.
Kirill Z. | Physics, math tutor with great knowledge and teaching skillsPhysics, math tutor with great knowledge...
4.9 4.9 (174 lesson ratings) (174)
0
Since sec(x)<0 and tan(x)>0, angle is in the third quadrant.

cot(x)=11/4
cos(x)=-√[1/(1+tan2(x))]=-√[1/(1+16/121)]=-11/√137;
sin(x)=-√[1-cos2(x)]=-√[1-121/137]=-4/√137
sec(x)=-(√137)/11
cosec(x)=-(√137)/4
Felice R. | Need Help in Math and Science - Engineer willing to helpNeed Help in Math and Science - Engineer...
4.0 4.0 (1 lesson ratings) (1)
0
Well if we use the trigonometric functions

sin X = opposite / hypotenuse
cos X = adjacent / hypotenuse