PLEASE HELP ASAP QUESTION IN DETAILS

Cos(−θ)=√3/3, sinθ<0

Delicious77 [7]

Answer:

$\sin\theta=-\frac{\sqrt{6}}{3}$

Step-by-step explanation:

The given trigonometric equation is $\cos(-\theta)=\frac{\sqrt{3} }{3}$ .

We can either use the Pythagorean identity or the right angle triangle to solve for $\sin\theta$ .

According to the Pythagorean identity,

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

Recall that, the cosine function is an even function, therefore

$\cos(-\theta)=\cos(\theta)$

$\Rightarrow \cos(\theta)=\frac{\sqrt{3} }{3}$ .

We substitute this value in to the above Pythagorean identity to get;

$(\frac{\sqrt{3}}{3})^2+\sin^2\theta=1$

$\Rightarrow \frac{3}{9}+\sin^2\theta=1$

$\Rightarrow \sin^2\theta=1-\frac{3}{9}$

$\Rightarrow \sin^2\theta=\frac{6}{9}$

$\Rightarrow \sin\theta=\pm \sqrt{\frac{6}{9}}$

$\Rightarrow \sin\theta=\pm \frac{\sqrt{6}}{3}$

But we were given that,

$\sin\theta\:$ , so we choose the negative value.

$\Rightarrow \sin\theta=-\frac{\sqrt{6}}{3}$

The correct answer is B

7 0

3 years ago

Working alone, it takes Julia 16 hours to clean an attic. Lea can clean the same attic in 15 hours. If they worked together how

egoroff_w [7]

How do you think we set this problem up?

7 0

3 years ago

9. PART A: Which of the following best summarizes

ivanzaharov [21]

Answer:

D Stanton encourages the audience to spread the word for their cause

Step-by-step explanation:

I just know I have done the test and it makes the most sense. :)

3 0

2 years ago

5 An army cook wants to make pudding

photoshop1234 [79]

Answer:

27

Step-by-step explanation:

First you dvide 864 by 4 to get 216. Next you multiply the 216 by 2 to find that there are 432 cups in 864 servings. Finally you divide by 16 to turn 432 cups into 27 gallons.

I hope this helps!

3 0

2 years ago

Read 2 more answers

Here are some prices customers paid for different items at a farmer’s market. Find the cost for 1 pound of each item.

posledela

Answer:

1 pounds of apples $=$ $\$ 1·25

1 pounds of cheese $=$ $\$ 7

1 pounds of coffee beans $=$ $\$ 5·5

1 pounds of fudge $=$ $\$ 9

1 pounds of pumpkin $=$ $\$ 0·88

Step-by-step explanation:

Unit Rate is the ratio between two different quantities with different units

The ratio of cost per items is

$=$ $\frac{dollars}{pounds}$

4 pounds of apples $= \$ 5

4 pounds $= \$ 5

Divided 4 both the side

1 pounds of apples $=$ $\$ 1·25

$\frac{1}{2}$ pounds of cheese $= \$ 3·50

$\frac{1}{2}$ pounds $= \$ 3·50

Divided $\frac{1}{2}$ both the side

1 pounds of cheese $=$ $\$ 7

$\frac{3}{2}$ pounds of coffe beans $= \$ 8·25

$\frac{3}{2}$ pounds $= \$ 8·25

Divided $\frac{3}{2}$ both the side

1 pounds of coffee beans $=$ $\$ 5·5

$\frac{3}{4}$ pounds of fudge $= \$ 6·75

$\frac{3}{4}$ pounds $= \$ 6·75

Divided $\frac{3}{4}$ both the side

1 pounds of fudge $=$ $\$ 9

$\frac{25}{4}$ pounds of pumpkin is $= \$ 5·50

$\frac{25}{4}$ pounds $= \$ 5·50

Divided $\frac{25}{4}$ both the side

1 pounds of pumpkin $=$ $\$ 0·88

8 0

3 years ago