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almond37 [142]
3 years ago
13

The angle \theta_1θ

Mathematics
1 answer:
enyata [817]3 years ago
8 0

Answer:

sin\theta_1 = \dfrac{\sqrt{217}}{19}

Step-by-step explanation:

It is given that:

cos\theta_1 = -\dfrac{12}{19}

And we have to find the value of sin\theta_1 = ?

As per trigonometric identities, the relation between sin\theta\ and \ cos\theta can represented as:

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

Putting \theta_1 in place of \theta Because we are given

sin^2\theta_1 + cos^2\theta_1 = 1

Putting value of cosine:

cos\theta_1 = -\dfrac{12}{19}

sin^2\theta_1 + (\dfrac{12}{19})^2 = 1\\\Rightarrow sin^2\theta_1 + \dfrac{144}{361} = 1\\\Rightarrow sin^2\theta_1 = 1-\dfrac{144}{361}\\\Rightarrow sin^2\theta_1 = \dfrac{361-144}{361}\\\Rightarrow sin^2\theta_1 = \dfrac{217}{361}\\\Rightarrow sin\theta_1 = +\sqrt{\dfrac{217}{361}}, -\sqrt{\dfrac{217}{361}}\\\Rightarrow sin\theta_1 = +\dfrac{\sqrt{217}}{19}, -\dfrac{\sqrt{217}}{19}

It is given that \theta_1 is in 2nd quadrant and value of sine is always positive in 2nd quadrant. So, the answer is.

\Rightarrow sin\theta_1 = \dfrac{\sqrt{217}}{19}

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Can someone help me I have two more other questions they are 15 points each I just posted them right now! Thanks so much
nlexa [21]

Answer:

$10 coins: 21

$20 coins: 24

Step-by-step explanation:

heyy me again

So we can create 2 equations where

x = number of $10 coins

y = number of $20 coins:

x + y = 45

10x + 20y = 690

we can move equation 1 around so that we can get a value of x

x = 45 - y

now we can substitute x into the second equation

10(45 - y) + 20y = 690

450 - 10y + 20y = 690

10y = 240

y = 24

Now plug in y back into the first equation

x = 45 - y

x = 45 - 24

x = 21

8 0
3 years ago
6% sales tax, hotel charges $265 find cost before tax?
Mama L [17]
265 x 0.06 = 15.9

265 - 15.9 = 249.1

249.1 is your answer

hope this helps
3 0
3 years ago
Read 2 more answers
3 times 1 times 5/3 pleaseeeeeee helpppp
Ierofanga [76]

Answer:

5

Step-by-step explanation:

3*1*5/3=5

5 0
2 years ago
56 divided by 8\11 hellpppp
liraira [26]
Since this is a division problem with a fraction, you must multiply by its reciprocal.
56 x 11/8:
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3 years ago
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Llana [10]
Answer:
2log₅(x) - 2log₅(4)

Explanation:
Note the following rules before we begin:
log(a) - log(b) = log(a/b)
2log(a) = log(a²)

Now, for the given, we will work backwards as follows:
log₅(x/4)² = 2 [ log₅(x) - log₅(4)] 
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Hope this helps :)

6 0
3 years ago
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