Thursday

September 18, 2014

September 18, 2014

Posted by **john 2020** on Thursday, March 18, 2010 at 11:16pm.

csc u=-6/5, tan u is greater than 0

Find cos u/2

- precal -
**Reiny**, Thursday, March 18, 2010 at 11:58pmcsc u = -6/5

sinu = -5/6

by Pythagoras, and knowing sin u is negative and tan u is positive

cosu = -√11/6

we know cosA = 1 - 2cos^2(A/2)

or

cosu = 1 - 2cos^2(u/2)

-√11/6 = 1 - 2cos^2(u/2)

2cos^2(u/2) = 1 + √11/6)

cos u/2 = √[(1 + √11/6)/2]

check my arithmetic,

- precal -
**john 2020**, Friday, March 19, 2010 at 12:03amcan u simplify the answer any more?????

- Correction - precal -
**Reiny**, Friday, March 19, 2010 at 12:15amI had the formula backwards, ...

Should have been

cos A = 2cos^2(A/2) - 1

or

cos u = 2cos^2 (u/2) - 1

-√11/6 + 1 = 2cos^2 (u/2)

-√[1 - √11/6)/2] = cos (u/2)

I picked the negative value, since we knew u was in III, so u/2 was in II, and in II the cosine is negative.

Since you wanted the "exact" value, there is no point simplifying the above answer.

- precal -
**john 2020**, Friday, March 19, 2010 at 12:17amthank u

**Answer this Question**

**Related Questions**

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

trig - FInd the exact value pf the 6 trig function of alpha Given: point (-2,-6...

Trig - 1. Establish the identity: sin(theta+3pi/2)=-cos(theta) 2. Find the exact...

precal - find the exact value of the expression: csc (tan^-1 3/3)

trig help much appreciated! :)) - 1. Find the complete exact solution of sin x...

Trig - Given that tan θ = - (√3/8) and θ is in QII, find the ...

Math- Trig - 1. Determine the exact value of cos^-1 (pi/2). Give number and ...

trig - find the exact value for each function tan pi/3 cos pi/4

TRIG/ALGEBRA - 1) Find the exact value. Use a sum or difference identity. tan (-...

Trig - Given that csc θ = -4 and tan θ > 0, find the exact value of...