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Alexxx [7]
3 years ago
13

For positive acute angles A and B, it is know that tan A= 8/15 and sin B= 11/61. Find the value of cos (a+b) in simplest form

Mathematics
1 answer:
iragen [17]3 years ago
7 0

Answer:

812/1037

Step-by-step explanation:

To solve this, we have to use trigonometric identities.

Cos (A + B) is given as Cos A Cos B - Sin A Sin B. And from the question, we have that

Tan A = 8/15.

We know that in a triangle, the Tan angle is represented Opp/Adj and thus the Opp is 8, and the Adj is 15. Using Pythagoras, we have

hyp² = opp² + adj²

hyp² = 8² + 15²

hyp² = 64 + 225

hyp² = 289

hyp = √289 = 17

The identity of Cos is Adj/Hyp and that of Sin is Opp/Hyp.

Cos A = 15/17

Sin A = 8/17

Repeating the same process for B, we have

Sin B = 11/61

adj² = hyp² - opp²

adj² = 61² - 11²

adj² = 3721 - 121

adj² = 3600

adj = √3600 = 60

Cos B = 60/61

Now, using the earlier stated trigonometric identity, we have

cos (a + b) = CosA CosB - SinA SinB

cos (a + b) = 15/17 * 60/61 - 8/17 * 11/61

cos (a + b) = 900/1037 - 88/1037

cos (a + b) = 812/1037

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A relative frequency table is made from data in a frequency table.
Yuki888 [10]

Answer:

The value of g in the relative frequency table is 33%.

Step-by-step explanation:

We are given the following information; A 4-column table with 3 rows. The first column has no label with entries likes A, B, total. The second column is labeled C with entries 20%, 32%, 51%. The third column is labeled D with entries g, 16%, 49%. The fourth column is labeled total with entries 53%, 47%, 100%.

Representing the above information in tabular form, we get;

                       C                  D                Total

       A            20%               g                 53%

       B             31%              16%              47%

     Total         51%              49%             100%

Now, after seeing the whole table, it is clear that value of g is given by;

                  20% + g = 53%

                    g = 53% - 20%

                    g = 33%

Hence, the value of g in the relative frequency table is 33%.

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Answer:

32.9

Step-by-step explanation:

  1. 4.2 × 7 = 29.4
  2. Plug 29.4 in: 29.4 - 10.4 ÷ 2 + 2.9 × 3
  3. 10.4 ÷ 2 = 5.2
  4. Plug 5.2 in: 29.4 - 5.2 + 2.9 × 3
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  6. Plug 8.7 in: 29.4 - 5.2 + 8.7
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I hope this helps!

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