how do you do this (1 Viewer)

[ta1g]

I dont have a clue how to do this can anyone help me?

solve: 2sin2B=√3, for 0° _< B _< 360° (_< means less than or equal to)


and also this one....

given that sin = 3/4 and 90° < feta sign <180° write down the exact value of sec feta.

 

[Porcia]

just put the 2 coefficient to the other side to make root 3 over 2, and use the triangles to solve that... dont forget since there is a sin2B, the domain is halfed.

 

[insert-username]

solve: 2sin2B=√3, for 0° _< B _< 360° (_< means less than or equal to)

sin 2B = √3/2 (divide both sides by two)

Since you're multiplying your angle by 2, you have to multiply your domain by two, so we're looking for angles between 0 and 720 degrees (when you divide your answer by two, you'll get answers back in your original domain).

Therefore, 2B = 60 degrees, 120 degrees, 420 degrees, and 480 degrees

Therefore B = 30 degrees, 60 degrees, 210 degrees, and 240 degrees.


given that sin = 3/4 and 90° < feta sign <180° write down the exact value of sec feta.

When sin Ө = 3/4, your angle is either 48 degrees 35 minutes or 131 degrees 25 minutes. You're told that Ө is between 90 degrees and 180, so your angle is 131 degrees 25 minutes. sec Ө = 1/cos Ө. The exact value of cos Ө is 1² - 3/4² (Pythargoras Theorem in the unit circle) = 7/16. Therefore the exact value of sec Ө is 16/7.

I hope that made some sort of sense.


I_F

 

[ta1g]

Therefore, 2B = 60 degrees, 120 degrees, 420 degrees, and 480 degrees

Therefore B = 30 degrees, 60 degrees, 210 degrees, and 240 degrees.

how do you get all those different values?

 

[insert-username]

You get them from your unit circle - When sin theta = √3/2, theta could be 60 degrees or 120 degrees (since sin is your y-value). But because your final angle is multiplied by two, you need to go around the circle once more - when you halve 420 degrees and 480 degrees, you get two results that are below 360.

It's a little hard to explain without a diagram, but I hope that helps out.


I_F

 

[carpediem]

something about the word "feta" makes me laughs

 

[klaw]

isn't it theta?

 

[mitsui]

i think it is feta

.___.

 

[insert-username]

It's a Greek letter - Ө = 'theta'


I_F

 

[klaw]

yes, usually used for angles

 

[ta1g]

You get them from your unit circle - When sin theta = √3/2, theta could be 60 degrees or 120 degrees (since sin is your y-value). But because your final angle is multiplied by two, you need to go around the circle once more - when you halve 420 degrees and 480 degrees, you get two results that are below 360.

It's a little hard to explain without a diagram, but I hope that helps out.


I_F

yep i get it now, thanks