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a_sh-v [17]
3 years ago
13

Determine the sine, cosine, and tangent of the angle.

Mathematics
2 answers:
lana [24]3 years ago
5 0

Answer: Option d.

Step-by-step explanation:

You need to use the trigonometric identities:

sin\theta=\frac{opposite}{hypotenuse}\\\\cos\theta=\frac{adjacent}{hypotenuse}\\\\tan\theta=\frac{opposite}{adjacent}

Identify the opposite side, the adjacent side and the hypotenuse in the right triangle:

opposite=9\\adjacent=12\\hypotenuse=15

Substituting these values into the corresponding identity, you get:

sin\theta=\frac{9}{15}\\\\cos\theta=\frac{12}{15}\\\\tan\theta=\frac{9}{12}

Cloud [144]3 years ago
4 0

Answer:

The correct answer is option d

Step-by-step explanation:

From the given figure we can see that, a right angled triangle.

<u>Points to remember </u>

Sinθ = Opposite side/Hypotenuse

Cosθ = Adjacent side/Hypotenuse

Tanθ = Opposite side/Adjacent side

Let the angle be θ

<u>To find sine, cosine, and tangent  </u>

Sinθ = Opposite side/Hypotenuse = 9/15

Cosθ = Adjacent side/Hypotenuse = 12/15

Tanθ = Opposite side/Adjacent side = 9/12

The correct answer is Option d

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7 0
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trapecia [35]

Answer:

See below

Step-by-step explanation:

Let the  2 roots be  A and A^2.

Then A^3 = c/a and A + A^2 = -b/a.

Using the identity a^3 b^3 = (a + b)^3 - 3ab^2 - 3a^2b:-

A^3 + (A^2)^3 =  ( A + A^2)^3 - 3 A.A^4 - 3 A^2. A^2

= (A + A^2)^3 - 3A*3( A + A^2)

Substituting:-

c/a + c^2/a^2 = (-b/a)^3 - 3 (c/a)(-b/a)

Multiply through by a^3:-

a^2c + ac^2 = -b^3 + 3abc

Factoring:-

ac(a + c) = 3abc - b^3

This is not the formula required in the question but let's see if the formula in the question reduces to this. If it does we have completed the proof.

a(c - b)^3 = a(c^3 - 3c^2b + 3cb^2 - b^3) = ac^3 - 3ac^2b + 3acb^2 - ab^3

c(a - b)^3 = c(a^3 - 3a^2b + 3ab^2 - b^3) = ca^3 - 3a^2bc + 3acb^2 - cb^3.

These are equal so we have

ca^3 - 3a^2bc + 3acb^2 - cb^3 = ac^3 - 3abc^2 + 3acb^2 - ab^3

The 3acb^2 cancel out so we have:-

a^3c - ac^3 =  3a^2bc - 3abc^2 + b^3c - ab^3

ac(a^2 - c^2) = 3abc( a - c) + b^3(c - a)

ac(a + c)(a -c) = 3abc(a - c) - b^3 (a - c)

Divide through by (a - c):-

ac(a + c) = 3abc - b^3 , which is the result we got earlier.

This completes the proof.

 

3 0
3 years ago
Read 2 more answers
julia and her friends are making kites out of paper. For each kite, they need a piece of paper that is \dfrac{65}{100} \text{ me
Alona [7]

Answer:

  260 cm

Step-by-step explanation:

Each 1/00 of a meter is 1 cm, so 65/100 meters is 65 cm. If that is the length of paper required for 1 kite, then 4 times that length will be required for 4 kites.

__

The paper required for 4 kites is ...

  (65 cm) × 4 = 260 cm

8 0
2 years ago
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