Math Help - Trigonometry (Pre-Cal)

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 $tan\theta$

So,

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

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

3. Here's the 2nd part:

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

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)

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

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

then

Find ALL solutions. No restrictions.

2sin[^2]2x=1

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

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

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

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