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kumpel [21]
3 years ago
5

If tan theta = 12/5 and cos theta < 0, what is sin theta ?

Mathematics
1 answer:
Talja [164]3 years ago
8 0
1 + tan ² Ф=sec²Ф
1+(12/5)²=sec²Ф
169/25=sec² Ф
sec Ф=⁺₋√(169/25)=⁺₋13/5

sec Ф=1/cos Ф ⇒cosФ=1/sec Ф
 cos Ф>0   ⇔  sec Ф>0  ⇔  sec Ф=+ 13/5

cos Ф=1/secФ
cos Ф=1 / 13/5=5/13

we can calculate the sin Ф, with this method.
sin²Ф + cos²Ф=1  ⇒ sin Ф=⁺₋√(1-cos² Ф)
sin Ф=⁺₋√[1-(5/13)²]=⁺₋12/13
like cos Ф>0 and tan Ф>0   ⇒ sin Ф>0 ⇒sin Ф=12/13

answer: d.12/13

other method
tan Ф=sin Ф / cos Ф
12/5=sin Ф / 5/13
sin Ф=(12/5)*(5/13)=12/13

answer: d.12/13

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snow_tiger [21]
L x - 2 l = l 4 + x l

Remember : Absolute is just the distance from zero.

Ex : l -4 l turns into 4, as it is 4 spaces away from zero on a number line :)

l x - 2 l turns into x + 2

l 4 + x l stays the same.

So, our equation now looks like this :

x + 2 = 4 + x

So, we're basically just trying to get x by itself.

So, subtract 2 from both sides.

x = 4 + x - 2

Then, subtract x from both sides.

x - x = 4 -2 

0 = 2

Therefore, there are no solutions to this equation :)

~Hope I helped!~
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3 years ago
How do I find the missing values to .. (4,y) and (0,5) m = 3 over 4​
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Answer:

(4,3) (4,5)

Step-by-step explanation:

7 0
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3 years ago
Maria took out an unsubsidized Stafford loan of $6,925 to pay for college. She plans to graduate in 4 years. The loan had a dura
Finger [1]

Answer:

$144.70

Step-by-step explanation:

Calculation to determine how much greater will the amount of interest capitalized be than the minimum amount that she could pay to prevent interest capitalization

First step is to determine the Interest only monthly repayments

Using this formula

I=Prt

where,

P=$6925

r=0.05/1

t=1

Let plug in the formula

I=6925*0.05/12

I= $28.854166666

Second step is to determine the amount she will owe after 4 years

Using this formula

S=P(1+r)n

Let plug in the formula

S=6925*(1+0.05/12)4*12

S=6925*(1+0.05/12)48

S=$8454.70

Third step is to determine the Interest part

Interest =8454.70 - 6925

Interest = $1529.70

Now let determine the how much greater will the amount of interest capitalized be

Interest capitalized=1529.70 - 1385.00

Interest capitalized =$144.70

Therefore how much greater will the amount of interest capitalized be than the minimum amount that she could pay to prevent interest capitalization is $144.70

4 0
3 years ago
Write an equation of a line that passes through (-12,-14) with slope 6
shusha [124]
Fill in the slope and that point in y=mx+b

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Y=6x + 58
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