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Maurinko [17]
3 years ago
11

If sin theta = -1/2 and lies in the third quadrant, what is the cos?

Mathematics
1 answer:
never [62]3 years ago
5 0
Sin angle that equals the 1/2 value is the 30 degree on the 1st Quadrant.

The angle of 30 degree on the 3rd Quadrant is equivalent to (formula and circle in the 1st photo) 180 + 30 = 210°.

So theta = 210° (3rd Quadrant) = 30° (1st Quadrant).

cos \: 30\degree = \sqrt{3} \div 2

Now just transfer the cos 30° to the 3rd Quadrant and the signal will be negative (as shown in the 2nd photo attached).

cos \: 210 \degree = - \sqrt{3} \div 2

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EXPAND AND SIMPLIFY<br>​
Anit [1.1K]

Answer:

5⁴a²

Step-by-step explanation:

(5³a³)÷5a-¹×5-²a²

5³a³÷5a-¹×5-²a²

5³a³÷5¹-²×a-¹+²

5³a³÷5-¹a

5³a³/5-¹a

5³-(-¹)a³-¹

5⁴a²

5 0
3 years ago
Help plsssssss homewrok do taday <br> -2x - 3y = 6
OlgaM077 [116]

Answer:

x=0/y=-2

y=0/x=-3

....∞

Step-by-step explanation:

6 0
3 years ago
30 degree triangles.. photo provided
Vsevolod [243]
The answer is going to be the second one
6 0
3 years ago
Read 2 more answers
In the expansion of (3a + 4b)8, which of the following are possible variable terms? Explain your reasoning. a2b3; a5b3; ab8; b8;
Fiesta28 [93]

We have to find the expansion of (3a+4b)^{8}

We will use binomial expansion to expand the given expression, which states that the expression (a+b)^{n} is expanded as :

(a+b)^{n}=^{n}C_{0}a^{n}+^{n}C_{1}a^{n-1}b+^{n}C_{2}a^{n-2}b^{2}+........^{n}C_{n}b^{n}

Now expanding (3a+4b)^{8} we get,

(3a+4b)^{8}=^{8}C_{0}(3a)^{8}+^{8}C_{1}(3a)^{7}(4b)+^{8}C_{2}(3a)^{6}(4b)^{2}+^{8}C_{3}(3a)^{5}(4b)^{3}+^{8}C_{4}(3a)^{4}(4b)^{4}+^{8}C_{5}(3a)^{3}(4b)^{5}+^{8}C_{6}(3a)^{2}(4b)^{6}+^{8}C_{7}(3a)(4b)^{7}+^{8}C_{8}(4b)^{8}

(3a+4b)^{8}=^{8}C_{0}(3)^{8}a^{8}+^{8}C_{1}(3)^{7}(4)(a^{7}b)+^{8}C_{2}(3)^{6}(4)^{2}(a^{6}b^{2})+^{8}C_{3}(3)^{5}(4)^{3}(a^{5}b^{3})+^{8}C_{4}(3)^{4}(4)^{4}(a^{4}b^{4})+^{8}C_{5}(3)^{3}(4)^{5}(a^{3}b^{5})+^{8}C_{6}(3)^{2}(4)^{6}(a^{2}b^{6})+^{8}C_{7}(3)(4)^{7}(ab^{7})+^{8}C_{8}(4)^{8}(b^{8})

So, the variables are a^{5}b^{3} , b^{8} , a^{4}b^{4} , a^{8}  , [tex] ab^{7}

5 0
3 years ago
Solve the inequality x + 2 1/2 &gt; -1/2. Graph the solution set on a number line.show your work.
antiseptic1488 [7]

Answer:

x > - 3

Step-by-step explanation:

x + 2\frac{1}{2} > - \frac{1}{2}      First turn 2\frac{1}{2} into an fraction since its easier. So it becomes \frac{5}{2}

x + \frac{5}{2} > - \frac{1}{2}

<u>   - </u>\frac{5}{2}<u>     - </u>\frac{5}{2}<u>  </u>       Do inverse operations, so subtract \frac{5}{2} from both sides.

    x > - \frac{6}{2}          Combine  - \frac{5}{2} with - \frac{1}{2}, which gives us - \frac{6}{2}

    x > - 3          Since we know that 6 divided by 2 is 3.

This would not allow me to attach an image so I am going to type a visual representation f what the graph would look like below)

<-------------O--------------------------------------------------->

-5    -4     -3      -2       -1     0     1     2    3    4     5

So, the number line would be a solid line rather than dashed (but I was not able to attach an image so I kind of had to improvise). When using ≥ ≤ sings the circle of the point is closed. When using < and > signs, the circle of the point is open. Thus, in this scenario since he sign is >, then the circle of the point is open. The direction of the arrow and ray for this equality is going to the right because the answer is that x is greater than - 3, Therefore any values greater than - 3 are a possibility which is why the arrow goes on indefinitely.

 

4 0
3 years ago
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