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3 years ago

Writing two column proofs

Mathematics

1 answer:

luda_lava [24]3 years ago

7 0

You have the right idea so far.

Use the fact that x = y and z = y to get x = z. We can use the transitive property or the substitution property (they are effectively the same idea).

Then you'll use the fact that w = x and w = t to get x = t. The same property is used here as well.

Lastly, connect x = z and x = t which will end up with t = z.

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Please help. How do you find cosine, sine, cosecant and secant with this triangle?

Veseljchak [2.6K]

Hi there! You have to remember these 6 basic Trigonometric Ratios which are:

sine (sin) = opposite/hypotenuse
cosine (cos) = adjacent/hypotenuse
tangent (tan) = opposite/adjacent
cosecant (cosec/csc) = hypotenuse/opposite
secant (sec) = hypotenuse/adjacent
cotangent (cot) = adjacent/opposite
cosecant is the reciprocal of sine
secant is the reciprocal of cosine
cotangent is the reciprocal of tangent

Back to the question. Assuming that the question asks you to find the cosine, sine, cosecant and secant of angle theta.

What we have now are:

Trigonometric Ratio
Adjacent = 12
Opposite = 10

Looks like we are missing the hypotenuse. Do you remember the Pythagorean Theorem? Recall it!

a²+b² = c²

Define that c-term is the hypotenuse. a-term and b-term can be defined as adjacent or opposite

Since we know the value of adjacent and opposite, we can use the formula to find the hypotenuse.

10²+12² = c²
100+144 = c²
244 = c²

Thus, the hypotenuse is:

$\large \boxed{c = 2 \sqrt{61} }$

Now that we know all lengths of the triangle, we can find the ratio. Recall Trigonometric Ratio above! Therefore, the answers are:

cosine (cosθ) = adjacent/hypotenuse = 12/(2√61) = 6/√61 = (6√61) / 61
sine (sinθ) = opposite/hypotenuse = 10/(2√61) = 5/√61 = (5√61) / 61
cosecant (cscθ) is reciprocal of sine (sinθ). Hence, cscθ = (2√61/10) = √61/5
secant (secθ) is reciprocal of cosine (cosθ). Hence, secθ = (2√61)/12 = √61/6

Questions can be asked through comment.

Furthermore, we can use Trigonometric Identity to find the hypotenuse instead of Pythagorean Theorem.

Hope this helps, and Happy Learning! :)

5 0

3 years ago

Explain how 9 x 4 can help you find 9 x 8

MrMuchimi

You can double the product of 9 and 4 to get to the product of 9 and 8

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3 years ago

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Make y the subject of the following equation.

Vedmedyk [2.9K]

Answer:

Step-by-step explanation:

if you subtract 5x then you will get y=-10-5x

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2 years ago

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Ryan's unpaid credit card balance was $1853.68. His APR is 24.9%. What is his new balance after he makes one new transaction for

nataly862011 [7]

Answer:

$2070.14

Step-by-step explanation:

Credit card terms vary, as do methods of computing interest and new balance. Here, we'll assume that no payment has been made (in violation of the terms of the credit card), and that the finance charge is only applied to the previous balance.

The finance charge is ...

$1853.68 × 0.249 ÷ 12 = $38.46 . . . . . . . the monthly rate is 0.249÷12

Then the new balance will be the sum of the previous balance, finance charge, and new transaction(s):

$1853.68 +38.46 + 178.00 = $2070.14

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Comment on lack of payment

Because no payment has been made, there may also be a late-payment charge added to the balance.

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3 years ago

Is my answer correct

Kryger [21]

Yes it is thirty because when u do 5×2×3 the correct answer turns out to be 30 $o yes!!!!!!

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2 years ago

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