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barxatty [35]
2 years ago
15

Simplify x = cos[2 arcsin(3/5)]. -7/25 7/25 4/5

Mathematics
1 answer:
Marina CMI [18]2 years ago
5 0

Answer:

7/25

Step-by-step explanation:

Let \theta= \arcsin(\frac{3}{5}) so we have x=\cos(2\theta)

As \cos(2\theta)=\cos^2\theta-\sin^2\theta, we'll have \cos[2\arcsin(\frac{3}{5})]=\bigr[\cos(\arcsin(\frac{3}{5}))\bigr]^2-\bigr[(\sin(\arcsin(\frac{3}{5}))\bigr]^2

To determine \cos(\arcsin(\frac{3}{5})), construct a right triangle with an opposite side of 3 and a hypotenuse of 5. This is because since \theta=\arcsin(\frac{3}{5}), then \sin\theta=\frac{3}{5}=\frac{\text{Opposite}}{\text{Hypotenuse}}. If you recognize the Pythagorean Triple 3-4-5, you can figure out that the adjacent side is 4, and thus, \cos\theta=\frac{4}{5}=\frac{\text{Adjacent}}{\text{Hypotenuse}}. This means that \cos(\arcsin(\frac{3}{5}))=\frac{4}{5}.

Hence, \cos[2\arcsin(\frac{3}{5})]=(\frac{4}{5})^2-(\frac{3}{5})^2=\frac{16}{25}-\frac{9}{25}=\frac{7}{25}

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After a storm, 135 trees out of 180 were left standing. What is the percentage loss of the number of trees?
beks73 [17]

Answer:

Percentage loss of the number of trees is 25\%.

Step-by-step explanation:

Given: After a storm, 135 trees out of 180 were left standing.

To find: What is the percentage loss of the number of trees?

Solution:

We have,

Total number of trees =180

Number of trees left standing =135

Therefore, loss of trees=180-135=45

We now that \text {Loss\%}=\frac{\text{Number of trees left}}{\text{Total number of trees}}\times 100 \%

\implies \text {Loss\%}=\frac{45}{180}\times 100 \%

\implies \text {Loss\%}=\frac{450}{18} \%

\implies \text {Loss\%}=25 \%

Hence, the percentage loss of the number of trees is 25\%.

6 0
3 years ago
Find m<1 in the rhombus below
Margarita [4]

Answer:

m \angle \: 1 = 120 \degree

Step-by-step explanation:

Given figure is of a rhombus.

Measures of the opposite angles of a rhombus are equal.

Therefore,

m \angle \: 1 = 120 \degree

6 0
2 years ago
-3 is a solution of y &gt; -2<br> true or false
BartSMP [9]
That is false.  When you look at a number line, -3 is to the left of -2.  A number to the left of another number is less than the number to the right. 
5 0
3 years ago
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A water pipe has a radius of 5 cm and a height of 7 cm. what volume of water does it take to fill the pipe?
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6 0
3 years ago
1d Round 103.459 to the nearest whole number.
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3 0
2 years ago
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