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Ulleksa [173]
3 years ago
10

Find sin theta if theta is an angle in standard position and the point with coordinates (3, -4) lies on the terminal side of an

angle.

Mathematics
1 answer:
alisha [4.7K]3 years ago
4 0

Answer:

\sin \theta=-\frac{4}{5}

Step-by-step explanation:

Given:

Angle is in standard position which means the starting ray is at the origin. The terminal side has coordinates (3, -4).

So, the 'x' value is 3 and 'y' value id -4.

Using Pythagoras Theorem, we find the hypotenuse.

Hypotenuse = \sqrt{3^2+(-4)^2}=\sqrt{9+16}=\sqrt{25}=5

Now, using the sine ratio for the angle, we have

\sin \theta=\frac{Opposite}{Hypotenuse}\\\sin \theta=\frac{-4}{5}\\\sin \theta=-\frac{4}{5}

Therefore, the value of \sin \theta is -\frac{4}{5}.

The value is negative as the point (3, -4) lies in the fourth quadrant and sine ratio is negative in the fourth quadrant,

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B.

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Answer: C,A,B

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7 0
2 years ago
Help asaaaaap please
katovenus [111]

Answer:

A. 1

General Formulas and Concepts:

<u>Pre-Algebra</u>

Order of Operations: BPEMDAS

  1. Brackets
  2. Parenthesis
  3. Exponents
  4. Multiplication
  5. Division
  6. Addition
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Equality Properties

Step-by-step explanation:

<u>Step 1: Define</u>

-5x - 1 ≤ -9

<u>Step 2: Solve for </u><em><u>x</u></em>

  1. Add 1 to both sides:                    -5x ≤ -8
  2. Divide -5 on both sides:             x ≥ 8/5

Here we see that any value <em>x</em> greater than or equal to 1.6 would work as a solution.

Therefore, our answer is A. 1, as it doesn't work as a solution.

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Find the critical value of t for a sample size of 23 and a 99% confidence level. choose the correct value from below:
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We can find critical value by using t - table.
For using t - table we need degree of freedom and alpha either for two tailed test or one tailed test.
We can determine degree of freedom by subtracting sample size from one.
So in given question sample size is 23. So we can say degree of freedom(df) for sample size 23 is
df = 23 - 1= 22
Now we have to go on row for degree of freedom 22.

After that we need to find alpha either for two tailed test or one tailedl test.
Confidence level is 99%. We can convert it into decimal as 0.99.

So alpha for two tailed test is 100 - 0.99 = 0.01

Alpha for one tailed test is 0.01/2 = 0.005.

So we will go on column for 0.01 for two tailed test alpha or 0.005 for one tailed test alpha.
 SO the critical value 22 degree of freedom and 0.01 two tailed alpha is 2.819 from t - table.

8 0
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