We have enabled User registrations.
0 votes
by
If tan(θ) = x/6 for − π/2 < θ < π/2 , find an expression for sin(2θ) in terms of x. Someone show how?

4 Answers

0 votes
by
selected by
 
Best answer

Start with the basic definition of tangent - opposite over adjacent. So x is opposite, 6 is adjacent. Since the hypotenuse = sqrt(a^2 + b^2), the hypotenuse is sqrt(x^2 + 36). Now we can define sin(θ) and cos(θ) as

sin(θ) = x / sqrt(x^2 + 36)

cos(θ) = 6 / sqrt(x^2 + 36)

The sin((2θ) = 2 sin(θ) cos(θ) so

sin(2θ) = 2 * [x/sqrt(x^2 + 36)] [6/sqrt(x^2 + 36)]

= 12x / (x^2 + 36)

I've verified this solution using Excel.

Lorem ipsum dolor sit amet, consectetur adipiscing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris nisi ut aliquip ex ea commodo consequat. Duis aute irure dolor in reprehenderit in voluptate velit esse cillum dolore eu fugiat.
SHOW ANSWER
0 votes
by

there's a formula: sin(2w)= 2tan(w)/1+tan(w)^2. just do that! we know tan(w)=x/6. plug in:

(x/3)/(1+x^2/36)=12x/(36+x^2) thats the answer

Lorem ipsum dolor sit amet, consectetur adipiscing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris nisi ut aliquip ex ea commodo consequat. Duis aute irure dolor in reprehenderit in voluptate velit esse cillum dolore eu fugiat.
SHOW ANSWER
0 votes
by

tan(?) = x/4 ? would desire to be in Quad. III considering the fact that tan(?) is helpful and attitude lies in -?/2 < ? < ?/2. sin(?) = -x/?(x^2 + sixteen) cos(?) = -4/?(x^2 + sixteen) sin(2?) = 2sin(?)cos(?) = 8x/(x^2 + sixteen)

Lorem ipsum dolor sit amet, consectetur adipiscing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris nisi ut aliquip ex ea commodo consequat. Duis aute irure dolor in reprehenderit in voluptate velit esse cillum dolore eu fugiat.
SHOW ANSWER
0 votes
by

tan(θ) = x/6

(sin(θ) + cos(θ))² = 1 + sin(2θ)

sin(θ) = x/√(36 - x²)

cos(θ) = 6/√(36 - x²)

(x + 6)²/(36 - x²) - 1 = sin(2θ)

= (x² + 12x + 36 - 36 + x²)/(36 - x²) = sin(2θ)

= (2x(x + 6))/(6 + x)(6 - x) = sin(2θ)

= 2x/(6 - x) = sin(2θ)

Lorem ipsum dolor sit amet, consectetur adipiscing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris nisi ut aliquip ex ea commodo consequat. Duis aute irure dolor in reprehenderit in voluptate velit esse cillum dolore eu fugiat.
SHOW ANSWER

Related questions

Welcome to TheBasicAnswers.com, where you can post questions and receive answers from other members of this portal. Please do not spam here. Spammers will be banned immediately. You can Contact us here
...