Wednesday

July 23, 2014

July 23, 2014

Posted by **Kayla** on Tuesday, October 16, 2007 at 11:10pm.

2 csc^2x = 3 cot^2x-1

- math -
**Reiny**, Wednesday, October 17, 2007 at 7:22amfirst change everything to sines and cosines

2/(sin^2 x) = 3(cos^2 x)/(sin^2 x) - 1

multiply by sin^2 x

2 = 3 cos^2 x - sin^2 x

but sin^2 x - 1 - cos^2 x

so

2 = 3 cos^2 x - 1 + cos^2 x

3 = 4cos^2 x

cos^2 x = 3/4

cos x = ±√3/2

Do you recognize the 1,√3,2 right-angled triangle? If not your calculuator should give you 30º.

if cos x = +√3/2 then x is in the first our fourth quadrants and

x = 30º or 330º

if cos x = -√3/2 then x is in the second and third quadrants and

x = 150º or 210º

(in radians the answers would be

pi/6, 11pi/6, 5pi/6,7pi/6)

**Related Questions**

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

Trigonometry - Hello all, In our math class, we are practicing the trigonometric...

Trigonometry - Use the trig Identities to find the other 5 trig functions. ...

math - use the quotient and reciprocal identities to simplify the given ...

verifying trigonometric identities - How do I do these problems? Verify the ...

trig 30 - For csc^2 A-1/cot A csc A, what is the simplest equivalent trig ...

Math - Perform the multiplication and use the fundamental identities to simplify...

trig - I do not understand these problems. :S I'd really appreciate the help. ...

trig - prove the identity: csc x-1/csc x+1 = cot^x/csc^x+2 csc x+1

Trig - Proving Identities: 2 columns (tan + cot)^2 = sec^2 + csc^2 I'm having ...