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Im stuck on a few questions...
Any ideas?
1) Solve the following equation for θ in the interval 0 ≤ θ ≤ 2π.
sin( 2 θ) +5/9 cos( θ) = 0
2) Solve
4 cos( 2 θ) = 1+tan( θ)
for θ in the interval −π/2 < θ < π/2.
3) Which of the following is equal to
(sin θ + cos θ)^2 + (sin θ − cos θ)^2 for all θ?
A) 2 cos(2 θ)
B) 2
C) 2 sin^2θ
D) cos(2 θ) − sin(2 θ)
E) 2 sin(2 θ)
1) sin( 2*beta ) + 5/9 * cos( beta ) = 0
sin( 2*beta ) = 2*sin( beta )*cos( beta )
sin( 2*beta ) + 5/9 * cos( beta ) = 2*sin( beta )*cos( beta ) + 5/9 * cos( beta ) = 0
cos( beta )*[ 2*sin( beta ) + 5/9 ] = 0
a) cos( beta ) = 0 => beta = pi/2 or beta = 3*pi/2
b) 2*sin( beta ) + 5/9 = 0
sin( beta ) = -5/18 => beta = arcsin( -5/18 ) ..... use calculator
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2) it is more complicated.... probably will solve it later
// i ' ve tried to solve it but it is complcated so the answer is very long and i didnt finished it, probably there is some faster way , some kind of trick...
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3)
the right answer is B) 2
( sin( beta ) + cos( beta ) )^2 + ( sin( beta ) - cos( beta ) )^2 =
= [ sin^2( beta ) + 2*sin( beta )*cos( beta ) + cos^2( beta ) ] + [ sin^2( beta ) - 2*sin( beta )*cos( beta ) + cos^2( beta ) ] =
= 2*( sin^2( beta ) + cos^2( beta ) ) = 2*1 = 2
Shouldnt there be 4 answers...or I could be way off...Quote:
Originally Posted by josipive
2 different answers for cos( beta ) = 0Quote:
Originally Posted by Maccabhoy
and 2 two different answers for arcsin( -5/18 )
for arcsin( -5/18 ) calculator will give you answer between -pi/2 and pi/2
but you have one more answer and that is arcsin( -5/18 ) - pi/2 ( I think )
also look at the first post to see answer for 3)
// not arcsin( -5/18 ) - pi/2 , but - pi - arcsin( -5/18 )
Thanks josipive.
The explanations are great!
Hello, Maccabhoy!
Here's the last one . . .
Did you even try to multiply it out ??Quote:
3) Which of the following is equal to ..for all
?
. .\;2\cos(2\theta) \qquad(B)\;2 \qquad <br />
(C)\;2\sin^2\!\theta \qquad (D)\;\cos(2\theta) - \sin(2\theta) \qquad(E)\;2\sin(2\theta))
. .
. .
Hmm... arcsin (-5/18) and - pi - arcsin( -5/18 ) are giving me wring answers.Quote:
Originally Posted by josipive
I am getting -0.28 and -2.86 respectively for these, but the quiz says they are wrong answers...and yes my calculator is in rad...
anyone know how figure this one out?
2) Solve
4 cos( 2 θ) = 1+tan( θ)
for θ in the interval −π/2 < θ < π/2.
dont know... on my calculator everything works fineQuote:
Originally Posted by Maccabhoy
1.angle ) arcsin( -5/18 )
2.angle ) -pi - arcsin( -5/18 ) // try -pi + arcsin( 5/18 ) that is the same