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2 years ago

Math question????????

Mathematics

1 answer:

mixer [17]2 years ago

7 0

Answer:

Answer C

Step-by-step explanation:

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First question, thanks. I believe there should be 3 answers

zysi [14]

Given: The following functions

$A)cos^2\theta=sin^2\theta-1$ $B)sin\theta=\frac{1}{csc\theta}$ $\begin{gathered} C)sec\theta=\frac{1}{cot\theta} \\ D)cot\theta=\frac{cos\theta}{sin\theta} \\ E)1+cot^2\theta=csc^2\theta \end{gathered}$

To Determine: The trigonometry identities given in the functions

Solution

Verify each of the given function

$\begin{gathered} cos^2\theta=sin^2\theta-1 \\ Note\text{ that} \\ sin^2\theta+cos^2\theta=1 \\ cos^2\theta=1-sin^2\theta \\ Therefore \\ cos^2\theta sin^2\theta-1,NOT\text{ }IDENTITIES \end{gathered}$

$\begin{gathered} sin\theta=\frac{1}{csc\theta} \\ Note\text{ that} \\ csc\theta=\frac{1}{sin\theta} \\ sin\theta\times csc\theta=1 \\ sin\theta=\frac{1}{csc\theta} \\ Therefore \\ sin\theta=\frac{1}{csc\theta},is\text{ an identities} \end{gathered}$

$\begin{gathered} sec\theta=\frac{1}{cot\theta} \\ note\text{ that} \\ cot\theta=\frac{1}{tan\theta} \\ tan\theta cot\theta=1 \\ tan\theta=\frac{1}{cot\theta} \\ Therefore, \\ sec\theta\ne\frac{1}{cot\theta},NOT\text{ IDENTITY} \end{gathered}$

$\begin{gathered} cot\theta=\frac{cos\theta}{sin\theta} \\ Note\text{ that} \\ cot\theta=\frac{1}{tan\theta} \\ cot\theta=1\div tan\theta \\ tan\theta=\frac{sin\theta}{cos\theta} \\ So, \\ cot\theta=1\div\frac{sin\theta}{cos\theta} \\ cot\theta=1\times\frac{cos\theta}{sin\theta} \\ cot\theta=\frac{cos\theta}{sin\theta} \\ Therefore \\ cot\theta=\frac{cos\theta}{sin\theta},is\text{ an Identity} \end{gathered}$

$\begin{gathered} 1+cot^2\theta=csc^2\theta \\ csc^2\theta-cot^2\theta=1 \\ csc^2\theta=\frac{1}{sin^2\theta} \\ cot^2\theta=\frac{cos^2\theta}{sin^2\theta} \\ So, \\ \frac{1}{sin^2\theta}-\frac{cos^2\theta}{sin^2\theta} \\ \frac{1-cos^2\theta}{sin^2\theta} \\ Note, \\ cos^2\theta+sin^2\theta=1 \\ sin^2\theta=1-cos^2\theta \\ So, \\ \frac{1-cos^2\theta}{sin^2\theta}=\frac{sin^2\theta}{sin^2\theta}=1 \\ Therefore \\ 1+cot^2\theta=csc^2\theta,\text{ is an Identity} \end{gathered}$

Hence, the following are identities

$\begin{gathered} B)sin\theta=\frac{1}{csc\theta} \\ D)cot\theta=\frac{cos\theta}{sin\theta} \\ E)1+cot^2\theta=csc^2\theta \end{gathered}$

The marked are the trigonometric identities

3 0

1 year ago

A cell phone costs $170 and has a tax rate of 7%. Write and Solve a proportion to find how much tax is paid on the cell phone.

Darina [25.2K]

Answer:

The Amount of tax paid on the cell phone is $11.9

Step-by-step explanation:

Given as :

The cost of the cell phone = x = $170

The tax rate of the cell phone = r = 7% of the phone cost

Let The Amount of tax paid on the cell phone = $y

<u>Now, According to question</u>

The Amount of tax paid on the cell phone = 7 % of cost of the cell phone

i.e y = 7% of x

Or, y = $\dfrac{7}{100}$ × x

Or, y = $\dfrac{7}{100}$ × $170

Or, y = $\frac{7\times 170}{100}$

∴ y = 7 × 1.7

i.e y = $11.9

So,The Amount of tax paid on the cell phone = y = $11.9

Hence, The Amount of tax paid on the cell phone is $11.9 Answer

4 0

2 years ago

a window is shaped like a semicircle and has diameter of 2 feet which expression describes the perimeter in feet of the window

mart [117]

Answer:

5.14 ft

Step-by-step explanation:

The perimeter of a circle is diameter X 3.14. since its half a circle, take the radius and multiply by 3.14. Since the radius is 1, the answer is pi itself. Then add 2 feet for the flat side of the semi-circle

3 0

2 years ago

HELP ME ANSWER THIS PLZ!!!!!!

alukav5142 [94]

Answer:

25% off $60 = $15

15% off $60 = $9 - 10%= $0.90

Step-by-step explanation:

$60 divided by 4= 25 x 4 = 100 is the whole number

6 0

3 years ago

Write an equation in slope-intercept form for the line that satisfies the following condition.

rosijanka [135]

Answer:

y = - x + 69

Step-by-step explanation:

Given the following :

Point on graph : (29, 8)

Equation of line ; y= 5x +17.

From the equation slope of line = 5

Intercept = 17

Slope of perpendicular line = - 1/5 ( negative reciprocal)

Using the equation :

y - y1 = m(x - x1)

From the Point given:

x1 = 29, y1 = 8

y - 8 = (- 1/5)(x - 29)

y - 8 = -1/5x + 29/5

y = -1/5x + 29/5 + 8

Multiply through by 5

y = - x + 29 +40

y = - x + 69

8 0

3 years ago