# Thread: trig: sin (θ) is 1/5. The value of cos^2 (θ) can be written.....

1. ## trig: sin (θ) is 1/5. The value of cos^2 (θ) can be written.....

The value of sin (θ) is 1/5. The value of cos^2 (θ) can be written in the form 6(α^2). Express the value of α^2 (alpha squared) as a fraction in simplest form.

2. Originally Posted by yoman360
The value of sin (θ) is 1/5. The value of cos^2 (θ) can be written in the form 6(α^2). Express the value of α^2 (alpha squared) as a fraction in simplest form.
$\displaystyle \cos ^2 \theta = 1 - \sin^2 \theta = 1 - \left( \frac15 \right)^2$

So if $\displaystyle 6 \alpha ^2 = 1 - \left( \frac15 \right)^2$, what is $\displaystyle \alpha^2$?

3. Originally Posted by Isomorphism
$\displaystyle \cos ^2 \theta = 1 - \sin^2 \theta = 1 - \left( \frac15 \right)^2$

So if $\displaystyle 6 \alpha ^2 = 1 - \left( \frac15 \right)^2$, what is $\displaystyle \alpha^2$?
I don't know what it is thats why I'm asking.

4. Originally Posted by Isomorphism
$\displaystyle \cos ^2 \theta = 1 - \sin^2 \theta = 1 - \left( \frac15 \right)^2$

So if $\displaystyle 6 \alpha ^2 = 1 - \left( \frac15 \right)^2$, what is $\displaystyle \alpha^2$?
Originally Posted by yoman360
I don't know what it is thats why I'm asking.
You are expected to show some effort at this stage. Where exactly are you stuck?

Can you do the arithmetic and simplify the right hand side of that expression? After doing that, what do you think the next step will be?

5. Originally Posted by mr fantastic
You are expected to show some effort at this stage. Where exactly are you stuck?

Can you do the arithmetic and simplify the right hand side of that expression? After doing that, what do you think the next step will be?
I'm sorry I wasn't really looking at it i just saw what is a^2

6. Originally Posted by Isomorphism
$\displaystyle \cos ^2 \theta = 1 - \sin^2 \theta = 1 - \left( \frac15 \right)^2$

So if $\displaystyle 6 \alpha ^2 = 1 - \left( \frac15 \right)^2$, what is $\displaystyle \alpha^2$?
$\displaystyle 6 \alpha ^2 = (25/25) - (1/25)$
$\displaystyle 6 \alpha ^2 = 24/25$
$\displaystyle \alpha ^2 = 4/25$

7. Originally Posted by yoman360
$\displaystyle 6 \alpha ^2 = (25/25) - (1/25)$
$\displaystyle 6 \alpha ^2 = 24/25$
$\displaystyle \alpha ^2 = 4/25$
Well Done