Please help me with these two problems!!

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

Nola purchased 2.5 pounds of cheese for 10. $50 her mother purchased 3 pounds of the same cheese for $12.60 the cost of the chee

Delvig [45]

The answer is 5.2 because if you do 12.60 - 10 it’s 2.6 so you add another 2.6 because it’s 2.6 for a half a pound so if you add the two half of pounds it will add up to one pound so it will be 2.6 + 2.6= 5.2 so basically 5.20$

6 0

3 years ago

Bianca's bank offers a savings account with a 2.1% APR, compounded monthly. What is the actual annual percentage yield on this a

Elanso [62]

2.1 x 12 = 25.2% is the percentage yield

5 0

2 years ago

Read 2 more answers

Select the correct answer. One factor of the polynomial 213 3r2 – 3x + 2 is (t – 2), which expression represents the other facto

Darina [25.2K]

Answer:

(x - 2)(x + 1)(2x -1)

Step-by-step explanation:

We use synthetic division as a tool for factoring the given expression. The coefficients of the terms given are {2, -3, -3, 2}. If x - 2 is a factor of this expression, then 2 is a root. We perform synthetic division as follows:

2 / 2 -3 -3 2

4 2 -2

-------------------------------

2 1 -1 0

Next, we determine whether or not (2x - 1)(x + 1) represents the remaining factor(s). Using -1 as divisor, we get:

-1 / 2 1 -1

-2 1

---------------------

2 -1 0

Since the remainder is zero, x + 1 must be a factor and (2x - 1) the third factor. Answer D is correct.

4 0

2 years ago

The line that goes horizantally (left to right) across the graph is called what? *

kodGreya [7K]

Step-by-step explanation:

horizontal line I believe

5 0

2 years ago