All categories

3 years ago

If cosA = 3/5 and A ∈ (630,720), find sin2A

Mathematics

1 answer:

Sergio039 [100]3 years ago

5 0

Answer:

- $\frac{24}{25}$

Step-by-step explanation:

Given 630 < A > 720 then A is in the fourth quadrant where

cosA > 0 and sinA < 0

Given

cosA = $\frac{3}{5}$ = $\frac{adjacent}{hypotenuse}$

Then the triangle is a 3- 4 - 5 with opposite side 4, thus

sinA = - $\frac{opposite}{hypotenuse}$ = - $\frac{4}{5}$

Using the trigonometric identity

sin2A = 2sinAcosA

= 2 × - $\frac{4}{5}$ × $\frac{3}{5}$

= $\frac{2(-4)(3)}{5(5)}$ = - $\frac{24}{25}$

You might be interested in

Write an equivalent expression for 25x - 45 using the properties of operations. Hint: find the GCF of 25 and 45. You use parenth

Oksana_A [137]

Answer:

25x - 45 = 5(5x - 9)

Step-by-step explanation:

Find the greatest common factor (GCF) of 25 and 45.

You can do this several ways, but one way is to list all the factors of both numbers and find the greatest common one:

Factors of 25: 1, 5, 25

Factors of 45: 1, 3, 5, 9, 15, 45

Therefore, 25 and 45 have 2 common factors: 1 and 5

So the greatest common factors is 5

25x - 45 = 5(ax - b)

To find the value of a, simply divide 25 by 5: 25 ÷ 5 = 5

To find the value of b, divide 45 by 5: 45 ÷ 5 = 9

25x - 45 = 5(5x - 9)

3 0

2 years ago

Graph the line that represents a proportional relationship between yyy and xxx where the unit rate of change of yyy with respect

My name is Ann [436]

Answer:

$y=\frac{4}{3}x$

The graph in the attached figure

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form $y/x=k$ or $y=kx$

In a proportional relationship the constant of proportionality k is equal to the slope m or unit rate of the line and the line passes through the origin

In this problem we have

$k=\frac{4}{3}$

substitute

$y=\frac{4}{3}x$

using a graphing tool

The graph in the attached figure

3 0

3 years ago

Read 2 more answers

Which statement is true about the product square root of 2(3square root of 2 + square root of 14)?

sukhopar [10]

Answer:

$\sqrt{2} (3\sqrt{2} +\sqrt{14})=6+2\sqrt{7}$

Step-by-step explanation:

Given : $\sqrt{2} (3\sqrt{2} +\sqrt{14})$

Solution:

$\sqrt{2} (3\sqrt{2} +\sqrt{14})$

$3*2+\sqrt{28})$

$6+2\sqrt{7}$

Thus , $\sqrt{2} (3\sqrt{2} +\sqrt{14})=6+2\sqrt{7}$

Thus the solution is irrational since square root 7 does not have a perfect square and equal to 6+2square root of 14

3 0

3 years ago

Read 2 more answers

PLEASE HELP/ANSWER! From 1980 to 1990, Lior’s weight increased by 25%. If his weight was k kilograms in 1990, what was it in 198

Elena-2011 [213]

The weight in 1980 is $\frac{4k}{5}$ kilograms

Solution:

From 1980 to 1990, Lior’s weight increased by 25%

His weight is "k" kilograms in 1990

To find: weight in 1980

This is a percentage increase problem

Let "x" be the weight in kilograms in 1980

The percentage increase is given by formula:

$\text{Percentage increase } = \frac{\text{Final value - initial value}}{\text{initial value}} \times 100$

Here,

Initial value in 1980 = x

Final value in 1990 = k

Percentage increase = 25 %

Substituting the values in formula,

$25 = \frac{k-x}{x} \times 100\\\\25x = 100(k-x)\\\\x = 4(k-x)\\\\x = 4k - 4x\\\\5x = 4k\\\\x = \frac{4k}{5}$

Thus the weight in kilograms in 1980 is $\frac{4k}{5}$

7 0

3 years ago

How do you show your work of 47 divided by 6?

saw5 [17]

Answer:

this is how you do it .

it doesn't have a end it just kept going

7 0

2 years ago