Really need you guys help on this problem... please help me

Please help me for the love of God if i fail I have to repeat the class

Elena-2011 [213]

$\theta$ is in quadrant I, so $\cos\theta>0$ .

$x$ is in quadrant II, so $\sin x>0$ .

Recall that for any angle $\alpha$ ,

$\sin^2\alpha+\cos^2\alpha=1$

Then with the conditions determined above, we get

$\cos\theta=\sqrt{1-\left(\dfrac45\right)^2}=\dfrac35$

and

$\sin x=\sqrt{1-\left(-\dfrac5{13}\right)^2}=\dfrac{12}{13}$

Now recall the compound angle formulas:

$\sin(\alpha\pm\beta)=\sin\alpha\cos\beta\pm\cos\alpha\sin\beta$

$\cos(\alpha\pm\beta)=\cos\alpha\cos\beta\mp\sin\alpha\sin\beta$

$\sin2\alpha=2\sin\alpha\cos\alpha$

$\cos2\alpha=\cos^2\alpha-\sin^2\alpha$

as well as the definition of tangent:

$\tan\alpha=\dfrac{\sin\alpha}{\cos\alpha}$

Then

1. $\sin(\theta+x)=\sin\theta\cos x+\cos\theta\sin x=\dfrac{16}{65}$

2. $\cos(\theta-x)=\cos\theta\cos x+\sin\theta\sin x=\dfrac{33}{65}$

3. $\tan(\theta+x)=\dfrac{\sin(\theta+x)}{\cos(\theta+x)}=-\dfrac{16}{63}$

4. $\sin2\theta=2\sin\theta\cos\theta=\dfrac{24}{25}$

5. $\cos2x=\cos^2x-\sin^2x=-\dfrac{119}{169}$

6. $\tan2\theta=\dfrac{\sin2\theta}{\cos2\theta}=-\dfrac{24}7$

7. A bit more work required here. Recall the half-angle identities:

$\cos^2\dfrac\alpha2=\dfrac{1+\cos\alpha}2$

$\sin^2\dfrac\alpha2=\dfrac{1-\cos\alpha}2$

$\implies\tan^2\dfrac\alpha2=\dfrac{1-\cos\alpha}{1+\cos\alpha}$

Because $x$ is in quadrant II, we know that $\dfrac x2$ is in quadrant I. Specifically, we know $\dfrac\pi2$ , so $\dfrac\pi4$ . In this quadrant, we have $\tan\dfrac x2>0$ , so

$\tan\dfrac x2=\sqrt{\dfrac{1-\cos x}{1+\cos x}}=\dfrac32$

8. $\sin3\theta=\sin(\theta+2\theta)=\dfrac{44}{125}$

6 0

3 years ago

What fraction is equivalent to 3/10 and has a denominator of 100

rosijanka [135]

Answer:

30/100

Step-by-step explanation:

This should be relatively easy since if the denominator is 100 then x/100 has to = 3/10

Since the denominator 10 has to be 100, you multiply by 10.

3 x 10 = 30

7 0

2 years ago

Read 2 more answers

What is the rule when you multiply several factors together? an even number of negative signs will result in

IrinaVladis [17]

⓵
When multiplying several factors together, an even number of negative signs will result in a positive answer.

↠ Because when you multiply two negative signs together, the negative signs turn into a positive sign, giving you a positive answer.

↠ If you have an even number of negative signs to multiply, then all your negative signs will be turned into positive signs, giving you a positive answer!

⓶
When multiplying several factors together, an odd number of negative signs will result in a negative answer.

↠ Because when you multiply a negative sign by a positive sign, the negative sign always wins, giving you a negative answer.

↠ If you har an odd number of negative signs to multiply, this means that once you are done multiplying all of the negative signs together except for the last one, you will be multiplying a positive sign with a negative sign.

↠ Here’s another way to see it : if you have 5 negative signs to multiply together, you will start by multiplying the first 2, which will give you a positive result. Then you will multiply the third and the fourth negative signs together, which will also give you a positive result. By that time, you will have two positive signs and one negative sign left, which means you will have no choice but to multiply a positive sign by the last negative sign, resulting in a negative answer!

I hope this helps! If you need a visual example, just tell me, it will be my pleasure! ☻

4 0

3 years ago

Anyone wanna play cod or 2k hop on rn

Thepotemich [5.8K]

Answer:

Sure

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers

Shanika makes 2800 milliliters if chicken soup for a dinner party she needs 3.5 liters how many more millileters does shanika ne

Liono4ka [1.6K]