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3 years ago

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An angle measures 120 degrees. Describe how to use special right triangles and the unit circle as tools to calculate the sine an

d cosine of this angle. please help!!!

1 answer:

natita [175]3 years ago

7 0

Answer:

120 degrees is the right angle and the 30 degree added which is 1/3 here we know as we can always divide a side measure by 90 then multiply by a second angle to find the hypotenuse. When we do this we are using a three way system just like a three way system appears when we use a right angle triangle and read the functions.

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I WILL GUVE BRAINLIEST!!!

sergey [27]

Answer:

$31.73\ in^2$

Step-by-step explanation:

1. Approach

The easiest way to solve this problem is to find the area of the triangle and the area of the inscribed circle. Then subtract the area of the inscribed circle from the area of the triangle.

2. Find the area of the triangle,

The area of the triangle can be found using the following formula,

$A_t=\frac{b*h}{2}$

Where (b) represents the base of the triangle, and (h) represents the height.

Substitute in the given values and solve,

$A_t=\frac{b*h}{2}\\\\A_t=\frac{12*10}{2}\\\\A_t=\frac{120}{2}\\\\A_t=60$

3. Find the area of the inscribed circle,

The formula to find the area of a circle is the following,

$A_c=(pi)r^2$

Where (pi) represents the numerical value (3.1415...) and (r) represents the radius of the circle. By its definition, the radius of a circle is always half of the diameter, thus the radius of the given circle is (3).

Substitute in the given values and solve,

$A_c=(pi)r^2\\\\A_c=(pi)(3)^2\\\\A_c=(pi)9\\\\A_c=28.26$

4. Find the area of the shaded region,

To accomplish this task, subtract the area of the circle from the area of the triangle,

$A_t-A_c=A_s$

$60-28.26=A_s$

$31.73=A_s$

8 0

3 years ago

If x - y = 10, then y =?

alexgriva [62]

Answer:

Given,x-y=10

Then,-y=10-x

or,-y=-(-10+x)

or,y=x-10

8 0

3 years ago

Please help solve!!! Thank you!!

Hatshy [7]

3 radical 11 ?? Maybe ??

5 0

3 years ago

Use euler’s method. i. e. to find the approximate values of the solution for yʹ=y(3−ty), y(0)=0. 5,h=0. 1, 0≤t≤0. 5

blsea [12.9K]

The approximate values of the solution by Euler's method is y₁=0.65, y₂=0.84, y₃=1.0778, y₄=1.3584, y₅=1.6921, y₆=2.05657.

In this question,

The differential equation is

yʹ=y(3−ty) ------- (1)

Here, y(0)=0. 5,h=0. 1, 0≤t≤0. 5.

By Euler's method,

$y_{n+1}=y_n+hf_n$

where $f_n=f(t_n,y_n)$

For, t = 0, y = 0,

$y_{1}=y_0+hf_0$ and

$f_0=f(t_0,y_0)$

Substitute in equation 1,

⇒ f(0,0.5) = 0.5(3-(0)(0.5))

⇒ f(0,0.5) = 0.5(3-0)

⇒ f(0,0.5) = 0.5(3)

⇒ f(0,0.5) = 1.5

Then, $y_{1}=y_0+hf_0$ becomes,

⇒ y₁ = 0.5 + (0.1)(1.5)

⇒ y₁ = 0.5 + 0.15

⇒ y₁ = 0.65

For, t = 1, y = 1,

$y_{2}=y_1+hf_1$ and

$f_1=f(t_1,y_1)$

⇒ f(0.1,0.65) = 0.65(3-(0.1)(0.65))

⇒ f(0.1,0.65) = 0.65(3-0.065)

⇒ f(0.1,0.65) = 1.90

Then, $y_{2}=y_1+hf_1$ becomes,

⇒ y₂ = 0.65+(0.1)(1.90)

⇒ y₂ = 0.84

For t = 2, y = 2,

$y_{3}=y_2+hf_2$ and

$f_2=f(t_2,y_2)$

⇒ f(0.2,0.84) = 0.84(3-(0.2)(0.84))

⇒ f(0.2,0.84) = 0.84(3-0.168)

⇒ f(0.2,0.84) = 2.3788

Then, $y_{3}=y_2+hf_2$

⇒ y₃ = 0.84+(0.1)(2.3788)

⇒ y₃ = 1.0778

For t = 3, y = 3,

$y_{4}=y_3+hf_3$ and

$f_3=f(t_3,y_3)$

⇒ f(0.3,1.0778) = 1.0778(3-(0.3)(1.0778))

⇒ f(0.3,1.0778) = 1.0778(3-0.32334)

⇒ f(0.3,1.0778) = 2.8848

Then, $y_{4}=y_3+hf_3$ becomes

⇒ y₄ = 1.0778+(0.1)(2.8848)

⇒ y₄ = 1.3584

For t = 4, y = 4,

$y_{5}=y_4+hf_4$ and

$f_4=f(t_4,y_4)$

⇒ f(0.4,1.3584) = 1.3584(3-(0.4)(1.3584))

⇒ f(0.4,1.3584) = 1.3584(3-0.5433)

⇒ f(0.4,1.3584) = 3.3372

Then, $y_{5}=y_4+hf_4$ becomes

⇒ y₅ = 1.3584 + (0.1)(3.3372)

⇒ y₅ = 1.6921

For t = 5, y = 5,

$y_{6}=y_5+hf_5$ and

$f_5=f(t_5,y_5)$

⇒ f(0.5,1.6921) = 1.6921(3-(0.5)(1.6921))

⇒ f(0.5,1.6921) = 1.6921(3-0.84605)

⇒ f(0.5,1.6921) = 3.6447

Then, $y_{6}=y_5+hf_5$ becomes

⇒ y₆ = 1.6921 + (0.1)(3.6447)

⇒ y₆ = 2.05657

Hence we can conclude that the approximate values of the solution by Euler's method is y₁=0.65, y₂=0.84, y₃=1.0778, y₄=1.3584, y₅=1.6921, y₆=2.05657.

Learn more about Euler's method here

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8 0

2 years ago

Solve for x: 7+4x=13+x

Mnenie [13.5K]

$7+4x=13+x \\\\4x-x=13-7 \\\\3x=6 \\\\\boxed{x=\frac{6}{3}=2}$

3 0

3 years ago

Read 2 more answers