This is a problem that requires solving a trigonometric equation.

[arizona_cards_11]

Trig Functions...

I don't really understand how my book wants me to approach this problem. And I know that you appreciate work...because this is for my benefit after all...but how exactly would this be worked?


Direction: Solve the equation for (theta)... 0 is less than or equal to (theta) < 2*pi

2sin^2(theta) = 1

The answers in the back of the book given in radians:

(theta) = (pi/4) , ((3*pi)/(4)) , ((5*pi)/(4)) , ((7*pi)/(4))

 

[d_leet]

This should be a pretty simple problem, what is the trouble you're having exactly? First solve for sin(theta), and then find all theta that satisfy that equation.

 

[arizona_cards_11]

2sin^2 (theta) = 1

sin^2(theta) = 1/2

sin(theta) = sqrt(1/2

? Those are my first few steps...are there any problems?

 

[d_leet]

Nope that is perfectly correct, now you just need to find the values of theta with sines of sqrt(1/2).

 

[arizona_cards_11]

I don't have a calculator with me so I'll have to wait until school...

The next question using same directions:

tan^2(theta) - tan(theta) = 0

 

[d_leet]

You might notice that this is a quadratic equation in tan(theta) so let x=tan(theta) and solve the resulting quadratic equation. Then you will have 2 equations to solve for tan(theta).

 

[arizona_cards_11]

okay...

x^2 - x = 0

(x-1)(x+0) = 0

x = 1 or x = 0

 

[arizona_cards_11]

Am I on the right track here?

 

[d_leet]

Am I on the right track here?

Yep so now you can substitute x=tan(theta) back in and find the values of theta such that those equations are satisfied.

 

[arizona_cards_11]

I'm a little bit confused on this point...

I plug tan(theta) back into (x-1)(x+0) ?

Thus, making... tan(theta) = 1 and tan(theta) = 0

 

[d_leet]

I'm a little bit confused on this point...

I plug tan(theta) back into (x-1)(x+0) ?

Thus, making... tan(theta) = 1 and tan(theta) = 0

No you had x=1 or x=0, from there put x=tan(theta) and then find the values of theta that will satisfy that.

 

[arizona_cards_11]

Is there any way to show your work besides plugging in...as my teacher is a stickler for descriptive work?

 

[d_leet]

Well I'm not really sure there are many wasy to show your work for this kind of a problem, but once you have it down to solving for theta, if you've memorized the important angles then it should be pretty simple to find what angles satisfy these conditions and then just explain that these are the angles satisfying the equations.

 

[arizona_cards_11]

The answers in the book are...

0 , (pi/4) , pi , ((5pi)/(4))

 

[HallsofIvy]

You are clearly expected to know the trig functions for some basic angles, not just use a calculator.

 

[navneet1990]

hey this stuff is easy
cant we use the identities
like

cos ( A-B) = cosA.cosB + sinA.sinB
and the other identities?

 

[shmoe]

2sin^2 (theta) = 1

sin^2(theta) = 1/2

sin(theta) = sqrt(1/2

? Those are my first few steps...are there any problems?

If sin^2(theta)=1/2 then you should have two possibilities for sin(theta), not just the one you have.