Posted by **natash** on Sunday, September 14, 2008 at 3:26am.

If tan(x)=8/3 and sin(x)<0, then find cos (x) sec(x) csc(x) i dont understand how u do this problem

- trig -
**David Q**, Sunday, September 14, 2008 at 6:09am
Think of the various definitions of these functions in terms of the height, base and hypoteneuse of a right-angled triangle. You're told that tan(x)=8/3, which means that the ratio of the height to the side is 8 to 3. So you can work out the hypoteneuse by Pythagoras. That should enable you to work out the other functions. Don't forget that condition about the sine of x being less than 0 though: there's more than one angle in a 360-degree circle with a tangent of 8/3, and you need to make sure you pick the right one.

- trig -
**drwls**, Sunday, September 14, 2008 at 10:45am
If tan x is positive and sin x is negative then yx must be in the third quadrant. For tan x = 8/3, the reference angle to the -x axis must be arcsin 8/sqrt(8^2 + 3^2) = 69.44 degrees. That means the angle x = 249.44 degrees. The cosine of that angle is -0.3512. The secant is the reciprocal of cosine. csc is the reciprocal of the sin, or -(sqrt73)/8

## Answer this Question

## Related Questions

more trig.... how fun!!!! - if you can't help me with my first question hopw you...

Confused! Pre-Cal - Verify that each equation is an identity.. tan A= sec a/csca...

Alg2/Trig - Find the exact value of the trigonometric function given that sin u...

trig 26 - simplify to a constant or trig func. 1. sec Ču-tan Ču/cos Čv+sin Čv ...

trigonometry repost - Reduce (csc^2 x - sec^2 X) to an expression containing ...

Pre-Calculus - I don't understand,please be clear! Prove that each equation is ...

Trig - Find the exact values of the six trigonometric functions 0 if the ...

Math - Trig - I'm trying to verify these trigonometric identities. 1. 1 / [sec(x...

Math-Trig - Trig Questions- 1. Write the algebraic expression which shows Cos((...

Trig - The question is: Set up a 2 column proof to show that each of the ...