What is 1.9 divided by 12?

Veseljchak [2.6K]

cos θ = $\frac{-4\sqrt{65} }{65}$ , sin θ = $\frac{-7\sqrt{65} }{65}$ , cot θ = 4/7, sec θ = $\frac{-\sqrt{65} }{4}$ , cosec θ = $\frac{-\sqrt{65} }{7}$

<h3>What are trigonometric ratios?</h3>

Trigonometric Ratios are values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle.

Sin θ: Opposite Side to θ/Hypotenuse

Tan θ: Opposite Side/Adjacent Side & Sin θ/Cos

Cos θ: Adjacent Side to θ/Hypotenuse

Sec θ: Hypotenuse/Adjacent Side & 1/cos θ

Analysis:

tan θ = opposite/adjacent = 7/4

opposite = 7, adjacent = 4.

we now look for the hypotenuse of the right angled triangle

hypotenuse = $\sqrt{7^{2} + 4^{2} }$ = $\sqrt{49+16}$ = $\sqrt{65}$

sin θ = opposite/ hyp = $\frac{7}{\sqrt{65} }$

Rationalize, $\frac{7}{\sqrt{65} }$ x $\frac{\sqrt{65} }{\sqrt{65} }$ = $\frac{7\sqrt{65} }{65}$

But θ is in the third quadrant(180 - 270) and in the third quadrant only tan and cot are positive others are negative.

Therefore, sin θ = - $\frac{7\sqrt{65} }{65}$

cos θ = adj/hyp = $\frac{4}{\sqrt{65} }$

By rationalizing and knowing that cos θ is negative, cos θ = - $\frac{-4\sqrt{65} }{65}$

cot θ = 1/tan θ = 1/7/4 = 4/7

sec θ = 1/cos θ = 1/ $\frac{4}{\sqrt{65} }$ = - $\frac{-\sqrt{65} }{4}$

cosec θ = 1/sin θ = 1/ $\frac{\sqrt{65} }{7}$ = $\frac{-\sqrt{65} }{7}$

Learn more about trigonometric ratios: brainly.com/question/24349828

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5 0

2 years ago

Help me please!!!!!!!!

Romashka [77]

Answer:

y = -6x - 5

Step-by-step explanation:

To find the equation using the point-slope equation, we need the slope and the y-intercept of the line

<u>Finding the slope of the line:</u>

We will calculate the slope between these 2 points: (-1 , 1) and (0 , -5)

Slope = Rise / Run

Rise of the line = y1 - y2

Rise = 1 - (-5)

Rise = 1 + 5

Rise = 6

Run of the line = x1 - x2

Run = -1 - 0

Run = -1

Slope of the line:

<em>Slope = Rise / Run</em>

<em>Slope = 6 / -1</em>

<u>Slope = -6 </u>

<u></u>

<u>Finding the y-intercept:</u>

y-intercept of a line is the y-ordinate of the point where the line intersect the y-axis

From the graph, we can see that the line intersects the y-axis at (0 , -5)

y-coordinate of the point = -5

<u>y-intercept = -5</u>

<u></u>

<u>Equation of the line:</u>

This is the general formula of the slope-intercept:

y = mx + b (where m is the slope of the line and b is the y-intercept )

Replacing the variables

y = (-6)x + (-5)

y = -6x - 5

4 0

3 years ago

There are 10 pieces of fruit in a fruit bowl. There are x bananas in the fruit bowl. All of the rest of the fruit are apples.

-BARSIC- [3]

The probability that Sarah takes one piece of each fruit is; (10x - x²)/100

<h3>Probability</h3>

We are given;

Number of fruits in the bowl = 10

Number of bananas = x

Thus, remaining fruits are;

Number of apples = 10 - x

Probability that at least one will be banana = x/10

Probability that at least one will be apple = (10 - x)/10

Thus;

Probability that she takes one piece of each fruit is;

x/10 × (10 - x)/10

⇒ x(10 - x)/100

⇒ (10x - x²)/100

Read more about probability at; brainly.com/question/251701

5 0

3 years ago

Elijah and 2 of his friends are each paid $20 per afternoon

aleksklad [387]

300 all together but 100 solo

6 0

3 years ago

Read 2 more answers

Am purchased a television that was originally $300. He had a coupon for 35% off all electronics. How much did the television cos

maria [59]

Answer: $206.70

Step-by-step explanation:

The coupon reduced the price of the television by 35% to:

= 300 * ( 1 - 35%)

= 300 * 65%

= $195

He then had to pay a 6% tax:

= Price * ( 1 + tax)

= 195 * ( 1 + 6%)

= 195 * 1.06

= $206.70

6 0

3 years ago