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alukav5142 [94]
3 years ago
11

2. Use the following picture for this question:

Mathematics
1 answer:
Art [367]3 years ago
4 0

Answer:

a.  24\sqrt{3}  and 41.6

b.  52.1

Step-by-step explanation:

a.

Considering the left side triangle the blue dotted side is the side "opposite" to the angle given and the side 24 is the side that is "adjacent" to the angle given. The trigonometric ratio tan relates opposite to adjacent. Also, let the blue dotted side be y.

<u>Note:</u> the exact value of tan 60 is \sqrt{3}

Thus, we can write Tan(60)=\frac{y}{24}\\y=24*Tan(60)\\y=24*\sqrt{3} \\y=24\sqrt{3}

Approximate value (rounded to nearest tenth):  24\sqrt{3} =41.6

b.

Considering the triangle to the right, the side "opposite" to the angle given (53 degrees) is 41.6 (just found in part (a)) and the side "hypotenuse" (side opposite to 90 degree angle) is x. The trigonometric ratio sine relates opposite and hypotenuse.

Thus we can write and solve:

Sin(53)=\frac{41.6}{x}\\x=\frac{41.6}{Sin(53)}=52.1

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How to prove this using trig identities?
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Step-by-step explanation:

tanB + cotB = (sinB)/(cosB) + (cosB)/(sinB)

 

                      = (sin2B + cos2B)/[(cosB)(sinB)]

 

                       = 1/[(cosB)(sinB)]

 

                        = (1/cosB)(1/sinB)

 

                        = (secB)(cscB)

7 0
3 years ago
How many solutions does the following equation have?<br> -17(y-2)=-17y+64−17(y−2)=−17y+64
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Answer:

Step-by-step explanation:

-17(y - 2) = -17y + 64

-17y  + 34 = -17y + 64

-17y + 17y = 64 - 34

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3 0
3 years ago
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The base of the right triangle drawn in the regular octagon measures 0.7 cm.
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Answer:

11.2

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a right triangle in an octagon is 1/2 a side length so to find the side length you must add .7 + .7. Next to find the perimeter of the octagon you must multiply the number of sides 8 by .14 which equals 11.2

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3 years ago
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Anyone know how to do trig? Given tan Ф = 4/5, find all other trig functions.
mars1129 [50]

9514 1404 393

Answer:

  • sin(Ф) = (4/41)√41; csc(Ф) = (√41)/4
  • cos(Ф) = (5/41)√41; sec(Ф) = (√41)/5
  • tan(Ф) = 4/5; cot(Ф) = 5/4

Step-by-step explanation:

The mnemonic SOH CAH TOA can help you with three of the functions. Then you need to remember the relations between those and the other three.

  Tan = Opposite/Adjacent

  tan(Ф) = 4/5

This suggests you can draw a triangle like the one attached that has adjacent side 5 and opposite side 4. Then hypotenuse can be found from the Pythagorean theorem:

  AC² = AB² +BC² = 5² +4² = 41

  AC = √41 . . . . . hypotenuse

Then the other trig functions are ...

  Sin = Opposite/Hypotenuse

  sin(Ф) = 4/√41 = (4/41)√41

  Cos = Adjacent/Hypotenuse

  cos(Ф) = 5/√41 = (5/41)√41

And the reciprocal functions are ...

  csc(Ф) = 1/sin(Ф) = (√41)/4

  sec(Ф) = 1/cos(Ф) = (√41)/5

  cot(Ф) = 1/tan(Ф) = 5/4

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3 years ago
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