Order the numbers −7, 2, −4, 8 from least to greatest

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

What happens when you subtract two negative numbers.

igomit [66]

Answer:

its still negative

Step-by-step explanation:

6 0

3 years ago

PLEASE HELP ILL GIVE BRAINLIEST!!!! I AM STUMPED AS I HAVE NOT PAYED ANY ATTENTION IN CLASS PLEASE HELP ME!!!!

Svetlanka [38]

Answer:

$y=\frac{-2}{3} x-15$

Step-by-step explanation:

First draw a line. I will put it in an attachment so you can see the line.

Now choose to points on the line to use the slope formula.

(0,15) and (3,13).

Slope formula: $\frac{y2-y1}{x2-x1}$

Plug in the information needed using the two points chosen.

$\frac{13-15}{3-0}=\frac{-2}{3}$

The slope is $\frac{-2}{3}$ .

Now use point-slope formula.

Point-slope formula: y-y1=m(x-x1)

y-15= $\frac{-2}{3}$ (x-0)

y-15= $\frac{-2}{3}$ x-0

Subtract 15 from both sides.

y= $\frac{-2}{3}$ x-15

Hope this helps!

If not, I am sorry.

5 0

2 years ago

A club can select one member to attend a conference. All of the club officers want to attend. There are a total of four officer

Shtirlitz [24]

Answer:

0.25

Step-by-step explanation:

Given that a club can select one member to attend a conference. All of the club officers want to attend. There are a total of four officers, and their designated positions within the club are President (P), Vice dash President (Upper V )comma Secretary (Upper S )comma nbspand Treasurer (Upper T ).

Sample space would be

a){ {P}, {V}, {S} {T}} is the sample space with notations standing for as given in the question

b) Each sample is equally likely. Hence we have equal chances for selecting any one out of the four.

If probability of selecting a particular sample of size I is p, the by total probability axiom we have

$4p =1\\p =0.25$

8 0

3 years ago

If rs=2x-1 and st=4x+7 then x=<br>rt=60

kirill [66]

Answer:

9

Step-by-step explanation:

<h3>Given</h3>

RS = 2x - 1
ST = 4x + 7
RT = 60
x= ?

<h3>Solution</h3>

Since S is the point on the line segment RT,

RT = RS + ST, and

60 = 2x - 1 + 4x + 7
60 = 6x + 6
10 = x + 1
x = 10 - 1
x = 9

5 0

4 years ago

Order the numbers −7​, 2​, −4​, 8 from least to greatest

Order the numbers −7, 2, −4, 8 from least to greatest