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ch4aika [34]
2 years ago
12

Rewrite each expression in terms of sine and cosine only.

Mathematics
1 answer:
Sliva [168]2 years ago
6 0

Answer:

1. Cosθ / SineθCosθ

2. Sineθ / Cos²θSineθ

3. Cosθ / Sineθ

4. Cos²θ + Sin²θ – Sin²θ

Step-by-step explanation:

1. SecθCotθ

Recall

Sec θ = 1/Cos θ

Cot θ = 1/Tan θ

But Tan θ = Sine θ / Cos θ

Thus,

Cot θ = 1 ÷ Sine θ / Cos θ

Cot θ = 1 × Cos θ / Sine θ

Cot θ = Cos θ / Sine θ

Therefore,

SecθCotθ = 1/Cos θ × Cos θ / Sine θ

SecθCotθ = Cosθ / SineθCosθ

2. SecθTanθCscθ

Recall

Sec θ = 1/Cos θ

Tan θ = Sine θ / Cos θ

Csc θ = 1/Sine θ

Thus,

SecθTanθCscθ =

1/Cosθ × Sineθ/Cosθ × 1/Sineθ

= Sineθ / Cos²θSineθ

3. Cscθ/Secθ

Recall

Csc θ = 1/Sine θ

Sec θ = 1/Cos θ

Thus,

Cscθ/Secθ = 1/Sine θ ÷ 1/Cos θ

= 1/Sine θ × Cos θ

= Cosθ / Sineθ

4. Cosθ / Secθ

Recall

Sec θ = 1/Cos θ

Cosθ / Secθ = Cosθ ÷ 1/Cosθ

= Cosθ × Cosθ

= Cos²θ

Recall

Cos²θ + Sin²θ = 1

Cos²θ = 1 – Sin²θ

But

1 = Cos²θ + Sin²θ

Thus,

Cos²θ = Cos²θ + Sin²θ – Sin²θ

Therefore,

Cosθ / Secθ = Cos²θ + Sin²θ – Sin²θ

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Item 20 A rectangular school banner has a length of 54 inches and a width of 36 inches. A sign is made that is similar to the sc
siniylev [52]

Answer:

The ratio of the area of the school banner to the area of the sign is <u>1944 cubic inches : 192.61 cubic inches.</u>

Step-by-step explanation:

Given:

A rectangular school banner has a length of 54 inches and a width of 36 inches. A sign is made that is similar to the school banner and has a length of 17 inches.

Now, to find the ratio of the area of the school banner to the area of the sign.

Dimensions of school banner :

Length = 54 inches.

Width = 36 inches.

Dimension of school sign:

Length = 17 inches.

So, to we find the width of sign by using cross multiplication method:

Let the width be x.

So, 54 is equivalent to 36.

Thus, 17 is equivalent to x.

\frac{54}{36} =\frac{17}{x}

By cross multiplying we get:

54x=612

Dividing both sides by 54 we get:

x=11.33\ inches.

Thus, the width of sign = 11.33 inches.

Now, to get the ratio of the area of the school banner to the area of the sign:

Area of the school banner : Area of the school sign.

= 54\times 36:17\times 11.33

= 1944:192.61

Therefore, the ratio of the area of the school banner to the area of the sign is 1944 cubic inches : 192.61 cubic inches.

6 0
3 years ago
Read 2 more answers
8+2(5 - x) = <br> Need help
nikdorinn [45]
We can distribute
2(5)+2(-x)=10-2x

we get
8+10-2x=?
18-2x=?

whatever that ? is, we don't know
multiply both sides by -1
2x-18=-?
add 18 to both sides
2x=18-?
divide bth sides by 2
x=9-(?/2)
whatever the left side  it, just divide it by 2 and subtract it from 9
7 0
3 years ago
How can you use the measures of center and the range to compare two populations?
DochEvi [55]

The measure of center and range to be used to compare the population is the median and the inter quartile range.

<u>Explanation:</u>

You utilize the median and the interquartile range (IQR) to portray skewed distributions of information. To look at two populaces, utilize the mean and the MAD when the two populations are symmetric. Utilize the middle and the IQR when possibly one or the two circulations are slanted.

In statistics and probability theory, the median is the worth isolating the higher half from the lower half of an information test, a populace or a likelihood circulation. For an informational collection, it might be thought of as the "center" esteem.

8 0
3 years ago
(m • n)-1 = <br> What is the answer to this question?
julsineya [31]
Fill in m and n with numbers then minus by one
6 0
3 years ago
Martha Alison and Scott buy 3.8 pounds of clay Martha used 1 /4 of the clay for a sculpture Scott used 2/5 of the remaining amou
Sever21 [200]

They are left with 0.51 pounds of clay.

Step-by-step explanation:

Given,

Amount of clay bought = 3.8 pounds

Amount used by Martha = \frac{1}{4}\ of\ clay

Amount used by Martha = \frac{1}{4}*3.8=0.95\ pounds

Amount left after Martha's use= Total amount - amount used by Martha

Amount left = 3.8 - 0.95 = 2.85 pounds

Amount used by Scott = \frac{2}{5}\ of\ amount\ left

Amount used by Scott = \frac{2}{5}*2.85=\frac{5.70}{5}

Amount used by Scott = 1.14 pounds

Amount left after Scott's use = Amount left after Martha's - Amount used by Scott

Amount left after Scott's use = 2.85 - 1.14 = 1.71 pounds

Amount used by Alison = 1.2 pounds

Amount left = Amount left after Scott's use - Amount used by Alison

Amount left = 1.71 - 1.2 = 0.51 pounds

They are left with 0.51 pounds of clay.

Keywords: subtraction, fraction

Learn more about subtraction at:

  • brainly.com/question/1577690
  • brainly.com/question/1578028

#LearnwithBrainly

3 0
3 years ago
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