1. ## Trigonometry (Pre-Cal)

Hello helpers!

I have been sitting here for about an hour and a half stumped on this question relating to trig expressions.

Factor and simplify the following:

tan(θ) x sin^2(θ) + tan(θ) x cos^2(θ)

then

Find ALL solutions. No restrictions.

2sin[^2]2x=1

Thank you for those of you who try to help me out! You are greatly appreciated!

-Margo

2. Originally Posted by margo98
Hello helpers!

I have been sitting here for about an hour and a half stumped on this question relating to trig expressions.

Factor and simplify the following:

tan(θ) x sin^2(θ) + tan(θ) x cos^2(θ)

then

Find ALL solutions. No restrictions.

2sin[^2]2x=1

Thank you for those of you who try to help me out! You are greatly appreciated!

-Margo

For the first one:
first factor out the $\displaystyle tan\theta$

So,

$\displaystyle tan\theta(sin^2 \theta + cos^2 \theta)$

Remember that $\displaystyle sin^2\theta + cos^2 \theta = 1$
Can you finish this one?

3. Here's the 2nd part:

$\displaystyle 2\sin^2{2x}=1$
$\displaystyle \sin{2x}=\pm\frac{1}{\sqrt{2}}$
since $\displaystyle \sin{\frac{(2n+1)\pi}{4}}=\pm\frac{1}{\sqrt{2}};n= 0,1,2,3,...$
$\displaystyle 2x=\frac{(2n+1)\pi}{4}$
$\displaystyle x=\frac{(2n+1)\pi}{8}$

4. Originally Posted by margo98
Hello helpers!

I have been sitting here for about an hour and a half stumped on this question relating to trig expressions.

Factor and simplify the following:

tan(θ) x sin^2(θ) + tan(θ) x cos^2(θ)

$\displaystyle \tan{t}(\sin^2{t} + \cos^2{t})$

you should know what $\displaystyle \sin^2{t} + \cos^2{t}$ equals.

then

Find ALL solutions. No restrictions.

2sin[^2]2x=1

$\displaystyle \sin^2(2x) = \frac{1}{2}$

$\displaystyle \sin(2x) = \pm \frac{1}{\sqrt{2}}$

$\displaystyle 2x$ = odd multiples of $\displaystyle \frac{\pi}{4}$

$\displaystyle x$ = odd multiples of $\displaystyle \frac{\pi}{8}$
hope it helps