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MaRussiya [10]
3 years ago
10

Find csc θ if cot θ = −21/20 and sin θ > 0.

Mathematics
1 answer:
Allushta [10]3 years ago
3 0
Note the answer must be positive because if sin>0, then csc > 0.
There are two ways to do this problem.
1) Use a trig identity:
csc^2 \theta = cot^2 \theta + 1
Sub in value for cot
csc^2 \theta = (-\frac{21}{20})^2 + 1 \\  \\ csc^2 \theta = \frac{841}{400} \\  \\ csc \theta = \frac{\sqrt{841}}{\sqrt{400}} = \frac{29}{20}

2) Use a right triangle and SOH CAH TOA
cot = 1/tan = adjacent/opposite = -21/20
Therefore adjacent side = 21, opposite side = 20
Use pythagorean thm to find hypotenuse:
\sqrt{21^2 + 20^2} = \sqrt{841} = 29

csc = 1/sin = hypotenuse/opposite = 29/20

Hope this helps.
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Find what the question asks. 200 points. Will mark brainleist
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Note:
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An entire circle has a central angle of 360°.

For the sector with radius = (3+4) = 7cm and a central angle of 120°, the area is
A_{1}= \frac{120}{360}*(49 \pi ) = \frac{49}{3} \pi \, cm^{2}

For the sector with radius =  3 cm and a central angle of 120°. the area is
A_{2}= \frac{120}{360} *(9 \pi ) = 3 \pi  \, cm^{2}

The area of the shaded sector (see the figure) is
A=A_{1}-A_{2} = ( \frac{49}{3} -3) \pi  =  \frac{40}{3} \pi  \, cm^{2}

Answer: \frac{40}{3}  \pi  \, cm^{2}


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3 years ago
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What is the measure of the smallest angle?<br> A 53<br> B 57<br> C 63<br> D 63
zhannawk [14.2K]

Answer:

A

Step-by-step explanation:

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What is the value of x in the equation 1.5(x + 4) – 3 = 4.5(x – 2)?
rjkz [21]
Hello!

Step 1: Simplify both sides of the equation.<span><span><span>
1.5<span>(<span>x+4</span>)</span></span>−3</span>=<span>4.5<span>(<span>x−2</span>)</span></span></span><span><span><span><span><span><span>

(1.5)</span><span>(x)</span></span>+<span><span>(1.5)</span><span>(4)</span></span></span>+</span>−3</span>=<span><span><span>(4.5)</span><span>(x)</span></span>+<span><span>(4.5)</span><span>(<span>−2</span>)</span></span></span></span>(Distribute)<span><span><span><span><span>

1.5x</span>+6</span>+</span>−3</span>=<span><span><span>4.5x</span>+</span>−9</span></span><span><span><span>

(<span>1.5x</span>)</span>+<span>(<span>6+<span>−3</span></span>)</span></span>=<span><span>4.5x</span>−9</span></span>(Combine Like Terms)<span><span><span>

1.5x</span>+3</span>=<span><span>4.5x</span>−9</span></span><span><span><span>
</span></span></span>Step 2: Subtract 4.5x from both sides.<span><span><span><span>

1.5x</span>+3</span>−<span>4.5x</span></span>=<span><span><span>4.5x</span>−9</span>−<span>4.5x</span></span></span><span><span><span>

−<span>3x</span></span>+3</span>=<span>−9</span></span>

Step 3: Subtract 3 from both sides.<span><span><span><span>

−<span>3x</span></span>+3</span>−3</span>=<span><span>−9</span>−3</span></span><span><span>

−<span>3x</span></span>=<span>−12</span></span>

Step 4: Divide both sides by -3.<span><span><span>

−<span>3x</span></span><span>−3</span></span>=<span><span>−12</span><span>−3</span></span></span><span>

x=<span>4

Hope this helps! Cheerio, and have a lovely day!</span></span>
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3 years ago
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7n+2 = 4n+17 solve the equation
lions [1.4K]

Answer:

n = -5

Step-by-step explanation:

Solve for n:

n + 2 = 4 n + 17

Hint: | Move terms with n to the left hand side.

Subtract 4 n from both sides:

(n - 4 n) + 2 = (4 n - 4 n) + 17

Hint: | Combine like terms in n - 4 n.

n - 4 n = -3 n:

-3 n + 2 = (4 n - 4 n) + 17

Hint: | Look for the difference of two identical terms.

4 n - 4 n = 0:

2 - 3 n = 17

Hint: | Isolate terms with n to the left hand side.

Subtract 2 from both sides:

(2 - 2) - 3 n = 17 - 2

Hint: | Look for the difference of two identical terms.

2 - 2 = 0:

-3 n = 17 - 2

Hint: | Evaluate 17 - 2.

17 - 2 = 15:

-3 n = 15

Hint: | Divide both sides by a constant to simplify the equation.

Divide both sides of -3 n = 15 by -3:

(-3 n)/(-3) = 15/(-3)

Hint: | Any nonzero number divided by itself is one.

(-3)/(-3) = 1:

n = 15/(-3)

Hint: | Reduce 15/(-3) to lowest terms. Start by finding the GCD of 15 and -3.

The gcd of 15 and -3 is 3, so 15/(-3) = (3×5)/(3 (-1)) = 3/3×5/(-1) = 5/(-1):

n = 5/(-1)

Hint: | Simplify the sign of 5/(-1).

Multiply numerator and denominator of 5/(-1) by -1:

Answer: n = -5

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3 years ago
Angle Sum Theorem. y = ?
salantis [7]

Answer:

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Step-by-step explanation:

Interior angles of ALL triangles sum to 180°

The whole large triangle has angles 60 60 60   ( they sum to 180)

that means x = 30

then the small triangle on the right has     60 + 30 + y = 180

  meaning y = 90 °

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1 year ago
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