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3 years ago

The angle e lies in Quadrant II.sin 0 = 3/4 What is cos O?

Mathematics

1 answer:

Vilka [71]3 years ago

4 0

Answer:

-√7/4

Step-by-step explanation:

Mathematically;

Sine is the ratio of opposite to hypotenuse

So here, hypotenuse is 4

The opposite is 3

To get the adjacent, we use the Pythagoras’ theorem which states that the square of the hypotenuse is equal the sum of the squares of the two other sides

Let the adjacent be x

4^2 = 3^2 + x^2

x^2 = 16-9

x^2 = 7

x = √7

The cosine is the ratio of the adjacent to the hypotenuse

Since we want to consider quadrant II

Cosine is negative here;

So the answer for Cos will be;

Cos theta = -√7/4

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3 years ago

Solve the equation; 3a/4-2a/3=7/4

DiKsa [7]

Answer: " a = 21 " .

_____________________

Step-by-step explanation:

Given: 3a/4-2a/3 = 7/4 ; Solve for "a" ;

Rewrite as: (3a/4) - (2a/3) = (7/4) ;

Now, for each of the three (3) "denominator values" in "fraction form" within the equation given:

→ Find the "LCD" ["Least Common Denominator"]:
The denominators are: 4, 3, and 4 ;

that is: "3" and "4" ;
____

To find the LCD: First; multiply the denominators: "4 * 3 = 12" .
So; the value "12" could be the LCD; so, the value for the LCD is no greater than "12" ; however, there could be a smaller value.
To determine the LCD:
List the multiples of the given denominators:
____
3: 3, 6, 9, 12, 15 .... ;
4: 4, 8, 12, 16... ;
____
We find that "12" is, in fact, the LCD of "3" and 4:
____
We can multiply each side of the equation by "12" ; to eliminate the "fractional values" :
____
$12*[\frac{3a}{4} - \frac{2a}{3}] = 12*[{\frac{7}{4}]$
____
Note the "distributive property" of multiplication:
→ a(b+c) = ab + ac ;

____

As such:
$12*[\frac{3a}{4} - \frac{2a}{3}] = 12*[{\frac{7}{4}]$ ;

____
Let us start with the "left-hand side" of the equation:
____
$12*[\frac{3a}{4} - \frac{2a}{3}]$ ;

= $[12*\frac{3a}{4}] + [-12 * \frac{2a}{3}]$ ;
= $[12*\frac{3a}{4}] - [12 * \frac{2a}{3}] ;$
____
Note: " $[12*\frac{3a}{4}]$ " ;

$= \frac{12}{1} * \frac{3a}{4}$ ;

→ The "12" cancels to a "3" ; and the "4" cancels to a "1" ;
since: "12÷4 = 3" ; and since: "4÷4 = 1" ;
→ and we can rewrite the "left-hand-side" expression as:
→ " $\frac{3}{1} * \frac{3a}{1}$ " ; which we can simplify as:

→ "3 * 3a" ; which we can simplify as: " 9a " .
then we have: " [12 * $\frac{2a}{3}$ ] " ;

which equals:
= " $\frac{12}{1} * \frac{2a}{3}$ " ;
Note: The "12" cancels out to a "4"; & the "3" cancels out to a "1" ;

→ {since: "(12 ÷ 3 = 4)"; & since: "(3 ÷ 3 = 1)" ;
____
→ And we can rewrite the expression as:
→ " $\frac{4}{1} *\frac{2a}{1}$ " ; which we can simplify as:
→ " 4 * 2a " ; which we can simplify/calculation as: " 8a " ;
Now, we can rewrite the expression of the "left-hand side"
of the equation as:
____
→ " [9a] − [8a] " ; (don't forget to carry down the "minus sign"!) ;
which we can simplify/calculate to get:
→ " [9a − 8a] " ; which we can further simplify/calculate;

→ to get:
→ " 1a " ; or: "a" —the value for which we wish to solve!
____
Now, let us examine the "right-hand side" of the equation:
____

→ " $\frac{12}{1} * \frac{7}{4}$ " ;
Note: The "12" cancels out to a "3" ; & the "4" cancels out to a "1" ;
→ {Since: "12 ÷4 = 3 " ; & since: "4 ÷ 4 = 1 "} ;

And we can rewrite the expression as:
→ " $\frac{3}{1} * \frac{7}{1}$ " ; which we can simplify as:
→ " 3 * 7 " ; which can simplify/calculate to get: " 21" ;
⇒ Now, let us rewrite the equation; by using our simplified values for both the "left-hand side" and the "right-hand side" of the equation; to solve for "a" :
⇒ a = 21 ;

→ which is the correct answer:
→ " a = 21 " .
____
Hope this helps!

____

6 0

2 years ago

The angle e lies in Quadrant II.sin 0 = 3/4 What is cos O?​

The angle e lies in Quadrant II.sin 0 = 3/4 What is cos O?