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natulia [17]
2 years ago
9

The angle θ1\theta_1 θ 1 ​ theta, start subscript, 1, end subscript is located in Quadrant II\text{II} II start text, I, I, end

text , and cos⁡(θ1)=−211\cos(\theta_1)=-\dfrac{2}{11} cos(θ 1 ​ )=− 11 2 ​ cosine, left parenthesis, theta, start subscript, 1, end subscript, right parenthesis, equals, minus, start fraction, 2, divided by, 11, end fraction . What is the value of sin⁡(θ1)\sin(\theta_1) sin(θ 1 ​ ) sine, left parenthesis, theta, start subscript, 1, end subscript, right parenthesis ?
Mathematics
1 answer:
melomori [17]2 years ago
6 0

Answer:

\dfrac{3\sqrt{13}}{11}

Step-by-step explanation:

Given that the angle \theta_1  is located in Quadrant II; and

\cos(\theta_1)=-\dfrac{2}{11}

In Quadrant II, x is negative and y is positive.

\cos(\theta)=\dfrac{Adjacent}{Hypotenuse},\sin(\theta)=\dfrac{Opposite}{Hypotenuse}\\$Adjacent=-2\\Hypotenuse=11\\

To find \sin(\theta_1), we first determine the opposite angle of \theta_1.

This will be done using the Pythagoras theorem.

Hypotenuse^2=Opposite^2+Adjacent^2\\11^2=Opposite^2+(-2)^2\\Opposite^2=121-4=117\\Opposite=\sqrt{117}=3\sqrt{13}

Therefore:

\sin(\theta_1)=\dfrac{Opposite}{Hypotenuse}=\dfrac{3\sqrt{13}}{11}

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t=- \frac{5}{8} - \frac{ \sqrt{713} }{8} or t=- \frac{5}{8} + \frac{ \sqrt{713} }{8}
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4 0
2 years ago
Simplify 4a³b² × 3a⁶b⁵​
Rasek [7]

Answer:

12a^9b^7

Step-by-step explanation:

Multiplying variables of the same base, will require you to add the exponents.

4a^3b^2 * 3a^6b^5

         4*3 =  12

a^3 * a^6 =   a^9

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12a^9b^7

4 0
2 years ago
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The function y = (x + 4)4 is a transformation of the graph of the parent function y = x4. How is the zero of the parent function
Musya8 [376]
The answer is C but not sure about it please double check it


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7 0
2 years ago
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If CX = 5 units, then DZ = ___ units
gulaghasi [49]

Answer:

DZ=4\ units

Step-by-step explanation:

we know that

If CD is parallel to XZ

then

Triangle XYZ is similar to Triangle YCD

therefore

The ratio of their corresponding sides are equal

\frac{XY}{CY}=\frac{ZY}{YD}

we have

CX=5\ units, CY=25\ units, YD=20\ units,

XY=CX+CY

XY=5+25=30\ units

ZY=YD+DZ

ZY=20+DZ

substitute the values

\frac{30}{25}=\frac{20+DZ}{20}

20\frac{30}{25}={20+DZ}

24={20+DZ}

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5 0
2 years ago
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Goshia [24]

Answer:

speed of Jada = 6km per hour which is not equal to

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Step-by-step explanation:

formula of speed = distance covered/ time taken

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time = 15 mins

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15 mins = 1/60 * 15 hour = 0.25 hours

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thus,

speed = 2km/(1/3)hour = 6  km per hour

Now we have

speed of Jada = 6km per hour which is not equal to

speed of Andre = 8km per hour

6 0
2 years ago
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