Homework Help: Trig

Posted by Jon on Friday, February 15, 2008 at 4:54pm.

Find the exact value of sin2(theta) if cos(theta) = -sqrt 5/3 and 180 < theta < 270.
A)-1/9
B)-4 sqrt 5/9
C)1/9
D)4 sqrt 5/9
B?

sin^2(theta) + cos^2(theta) = 1
sin^2(theta) = 1 - cos^2(theta)
sin^2(theta) = 1 - (sqrt 5/3)^2
sin^2(theta) = 1 - (sqrt 25/9)

Trig - Reiny, Friday, February 15, 2008 at 5:07pm
You are getting a lot of these wrong lately.

(I am going to use sinx for your sin(theta)

since cosx = √5 /3
using Pythagoras I found the other side ot the triangle to be 2.
But we are in the third quadrant so sinx =-2/3

then sin 2x = 2sinxcosx
= 2(-2/3)(-√5/3)
= 4√5/3 which is D

with a calculator, you could have easily checked that your choice and the others beside D would not work.
- Trig - Reiny, Friday, February 15, 2008 at 5:13pm
  oops, sorry type
  
  make 4√5/3 which is D
  read : 4√5/9 which is D
Trig - Jon, Friday, February 15, 2008 at 5:15pm
I really thought I had that one.
My 1st thought was D but I figured since sqrt 5/3 was negative then so would my final answer.
- Trig - Reiny, Friday, February 15, 2008 at 5:23pm
  Are you familiar with the CAST rule, that is, do you know which ratios are negative in which quadrants??
Trig - Jon, Friday, February 15, 2008 at 5:26pm
No

Answer this Question

Related Questions

easy trig - If sin(theta)=[sqrt(70)]/7 and theta is in Quadrant two, find the ...
simple trig - If sin(theta)=[sqrt(70)]/7 and theta is in Quadrant two, find the ...
Trig(3 all with work) - 1)Find the exact value of cos 105 by using a half-angle ...
Pre Calc. - Use the sum or difference identity to find the exact value of sin255...
Precalculus check answers help! - 1.) Find an expression equivalent to sec theta...
Precalculus check answers help! - 1.) Find an expression equivalent to sec theta...
Algebra II - Multiple Choice (theta) means the symbol 0 with the dash in it. 1.)...
Trig(continued) - 2)Find the solution of sin2 theta = cos theta if 0 -< ...
Precalculs - I have no idea how to do these type of problems. -------Problem...
Trig - Solve the following interval 0<_ (less than or equal to)0(Theta)&...

For Further Reading

First Name:
School Subject:
Answer: