trigonometry

Given tanx=8/15 when pi < x < 3pi/2, find tan x/2.

1. 👍 0
2. 👎 0
3. 👁 63
1. Use tan (2A) = 2tanA/(1 - tan^2 A)
or tanx = 2tan (x/2)(1 - tan^2 (x/2)) , let tan x/2 = y for easier typing
8/15 = 2y/(1 - y^2)
30y = 8 - 8y^2
8y^2 + 30y - 8 = 0
4y^2 + 15y - 4 = 0
(4y - 1)(y + 4) = 0
y = 1/4 or y = -4
tan x/2 = 1/4 or tan x/2 = -4
but x was in quadrant III , so x/2 must be in quadrant II
and in II, the tangent is negative,
so tan x/2 = -4

1. 👍 0
2. 👎 0
posted by Reiny
2. if tanx = 8/15 in QIII then
sinx = -8/√161
cosx = -15/√161
so
tanx/2 = (1-cosx)/sinx = (1 + 8/√161)/(-15/√161) = -(8+√161)/15
makes sense, since x/2 will be in QII where tangent is negative

1. 👍 0
2. 👎 0
3. oops - go with Reiny.
Do you see my mistake?

1. 👍 0
2. 👎 0
4. Tanx = -8/-15 = 8/15.
X = 28.1o S. of W. (Q3). = 208.1o CCW.
x/2 = 208.1/2 = 104o CCW = 76o N. of W.
Tan(x/2) = Tan104 = -4.0.

1. 👍 0
2. 👎 0
posted by henry2,

Similar Questions

1. pre-calc

Can someone help me find the exact value of 4csc(3pi/4)-cot(-pi/4)? Thanks! cotx =1/tanx cscx = 1/sinx If you find it easier to conceptualize in degrees, realize that pi/4 radians is 45º and 3pi/4 is then 135º If you know the

asked by sarah on May 5, 2007
2. Trigo

Given that a^2+b^2=2 and that (a/b)= tan(45degee+x), find a and b in terms of sinx and cosx. I don't know what i'm supposed to do, and i don't come to an answer! Help, thanks! my workings: tan(45+x)= (1+tanx)/(1-tanx) a/b =

asked by Marrion on September 26, 2009
3. Trigonometry

Given that a^2+b^2=2 and that (a/b)= tan(45degee+x), find a and b in terms of sinx and cosx. I don't know what i'm supposed to do, and i don't come to an answer! Help, thanks! my workings: tan(45+x)= (1+tanx)/(1-tanx) a/b =

asked by Marrion on September 27, 2009
4. trigonometry (please double check this)

Solve the following trig equations. give all the positive values of the angle between 0 degrees and 360 degrees that will satisfy each. give any approximate value to the nearest minute only. a.) ( I got confused doing this 1 can

asked by anon on March 3, 2011
5. Trigonometry

Find the exact value of tan(a-b) sin a = 4/5, -3pi/2

asked by Dee on November 8, 2010
6. Math

1)A piano tuner uses a tuning fork. If middle C has a frequency of 264 vibrations per second, write an equation in the form d=sinw(t) for the simple harmonic motion. 2) Verify the identity tan^2X-cot^2X/tanX+cotX=tanX-cotX I'm not

asked by Lisa on October 9, 2006
7. Pre-Cal

Perform the addition or subtraction. tanx - sec^2x/tanx tan^2(x)/tan(x) - sec^2x/tanx = tan^2x sec^2x / tanx then I use the identity 1+tan^2u=sec^2u I do not know what to do at this point.

asked by Hannah on March 5, 2010
8. Math

Could someone explain the steps for this question. Simplify the expression tan(5pi/8)-tan(3pi/8)/1+tan(5pi/8)tan(3pi/8)

asked by Jake on January 24, 2012
9. Calculus - Integration

Hello! I really don't think I am understanding my calc hw. Please help me fix my errors. Thank you! 1. integral from 0 to pi/4 of (tanx^2)(secx^4)dx It says u = tan x to substitute So if I use u = tan x, then my du = secx^2 then I

asked by Shelley on January 29, 2007
10. Pre Cal

could someone please tell me what the other angle identity of tan is? Thank you much! "...other angle identity of tan x"? in relation to which "other" ? there are many identities dealing with the tangent. The most important is

asked by Marie on May 23, 2007

More Similar Questions