# trig

posted by .

How do you find the exact values of sin(u/2), cos(u/2), and tan(u/2) of tan(u)=-5/8

• trig -

since the tangent is negative, angle u is either in quadrant II or IV.
I made a diagram of a right-angled triangle with a hypotenuse of √89

we know
cos 2A = 2cos^2 A -1 or 1 - 2sin^2 A

so cos u = 2cos^2 (u/2) - 1
-8/√89 + 1 = 2cos^2 (u/2)
(√89 - 8)/(2√89) = cos^2 (u/2)
cos (u/2) = ± √(√89 - 8)/(2√89)

for the sine:
cos u = 1 - 2sin^2 (u/2)
2sin^2 (u/2) = 1 + 8/√89
sin^2 (u/2) = (√89+8)/(2√89)
sin (u/2) = ±√(√89+8)/(2√89)

Now sorting out the ±

IF u was in quadrant II, then u/2 is in quadrant I and both the sine and cosine would be positive.

If u was in quadrant IV, the u/2 is in quadrant II
and the sine would be positive and the cosine negative.

Since tanx = sinx/cosx
for tan (u/2) divide the above results, using the appropriate ± values.
Notice since both the sin (u/2) and cos (u/2) have 2√89 in the denominator, that part will cancel when you do the division.

## Similar Questions

1. ### Trig

Given: cos u = 3/5; 0 < u < pi/2 cos v = 5/13; 3pi/2 < v < 2pi Find: sin (v + u) cos (v - u) tan (v + u) First compute or list the cosine and sine of both u and v. Then use the combination rules sin (v + u) = sin u cos …
2. ### trig 26

simplify to a constant or trig func. 1. sec ²u-tan ²u/cos ²v+sin ²v change expression to only sines and cosines. then to a basic trig function. 2. sin(theta) - tan(theta)*cos(theta)+ cos(pi/2 - theta) 3. (sec y - tan y)(sec y + …
3. ### math

use exact values of the sin,cos and tan of (pi/3) and (pi/6)(which I have found)and the symmetry of the graphs of sin,cos and tan to find the exact values of sin(-pi/6), cos(5pi/3) and tan (4pi/3). I know that sin -(pi/6) = -1/2 and …
4. ### math

use exact values of the sin,cos and tan of (pi/3) and (pi/6)(which I have found)and the symmetry of the graphs of sin,cos and tan to find the exact values of sin(-pi/6), cos(5pi/3) and tan (4pi/3). I know that sin -(pi/6) = -1/2 and …
5. ### math

Use the exact values of the sin, cos and tan of pi/3 and pi/6, and the symmetry of the graphs of sin, cos and tan, to find the exact values of si -pi/6, cos 5/3pi and tan 4pi/3. I have found the answers to the first three using the …
6. ### math

Use the exact values of the sin, cos and tan of pi/3 and pi/6, and the symmetry of the graphs of sin, cos and tan, to find the exact values of sin -pi/6, cos 5/3pi and tan 4pi/3. I have found the answers to the first three using the …
7. ### precalculus

For each of the following determine whether or not it is an identity and prove your result. a. cos(x)sec(x)-sin^2(x)=cos^2(x) b. tan(x+(pi/4))= (tan(x)+1)/(1-tan(x)) c. (cos(x+y))/(cos(x-y))= (1-tan(x)tan(y))/(1+tan(x)tan(y)) d. (tan(x)+sin(x))/(1+cos(x))=tan(x) …
8. ### trig help much appreciated! :))

1. Find the complete exact solution of sin x = . 2. Solve cos 2x – 3sin x cos 2x = 0 for the principal value(s) to two decimal places. 3. Solve tan2 x + tan x – 1 = 0 for the principal value(s) to two decimal places. 4. Prove that …
9. ### Trigonometry desperate help, clueless girl here

2. solve cos 2x-3sin x cos 2x=0 for the principal values to two decimal places. 3. solve tan^2 + tan x-1= 0 for the principal values to two decimal places. 4. Prove that tan^2(x) -1 + cos^2(x) = tan^2(x) sin^2 (x). 5.Prove that tan(x) …
10. ### Precalculus

I am trying to submit this homework in but i guess i'm not doing it in exact values because it is not accepting it. I know i'm supposed to be using half angle formulas but maybe the quadrants are messing me up. Please help! Find sin …

More Similar Questions