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3 years ago

7

What is the solution to this inequality?

1 answer:

Ksivusya [100]3 years ago

4 0

The answer is D.

X/-5 = 2
x =2 * -5
Therefore, x is less than -10

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Given that sin(30)=1/2 and cos(30)=(sqrt3)/2, use trigonometric identities to find the value of cot(30)

Anit [1.1K]

<u>Your question: </u>given that sin(30)=1/2 and cos(30)=(sqrt3)/2, use trigonometric identities to find the value of cot(30)

The correct answer would be D $\sqrt{3}$

5 0

3 years ago

i f N(-7,-1) is a point on the terminal side of ∅ in standard form, find the exact values of the trigonometric functions of ∅.

Natali [406]

Answer:

$sin\ \varnothing = \frac{-1}{10}\sqrt 2$

$cos\ \varnothing = \frac{-7}{10}\sqrt 2$

$tan\ \varnothing = \frac{1}{7}$

$cot\ \varnothing = 7$

$sec\ \varnothing = \frac{-5}{7}\sqrt 2$

$csc\ \varnothing = -5\sqrt 2$

Step-by-step explanation:

Given

$N = (-7,-1)$ --- terminal side of $\varnothing$

Required

Determine the values of trigonometric functions of $\varnothing$ .

For $\varnothing$ , the trigonometry ratios are:

$sin\ \varnothing = \frac{y}{r}$ $cos\ \varnothing = \frac{x}{r}$ $tan\ \varnothing = \frac{y}{x}$

$cot\ \varnothing = \frac{x}{y}$ $sec\ \varnothing = \frac{r}{x}$ $csc\ \varnothing = \frac{r}{y}$

Where:

$r^2 = x^2 + y^2$

$r = \sqrt{x^2 + y^2$

In $N = (-7,-1)$

$x = -7$ and $y = -1$

So:

$r = \sqrt{(-7)^2 + (-1)^2$

$r = \sqrt{50$

$r = \sqrt{25 * 2$

$r = \sqrt{25} * \sqrt 2$

$r = 5 * \sqrt 2$

$r = 5 \sqrt 2$

<u>Solving the trigonometry functions</u>

$sin\ \varnothing = \frac{y}{r}$

$sin\ \varnothing = \frac{-1}{5\sqrt 2}$

Rationalize:

$sin\ \varnothing = \frac{-1}{5\sqrt 2} * \frac{\sqrt 2}{\sqrt 2}$

$sin\ \varnothing = \frac{-\sqrt 2}{5*2}$

$sin\ \varnothing = \frac{-\sqrt 2}{10}$

$sin\ \varnothing = \frac{-1}{10}\sqrt 2$

$cos\ \varnothing = \frac{x}{r}$

$cos\ \varnothing = \frac{-7}{5\sqrt 2}$

Rationalize

$cos\ \varnothing = \frac{-7}{5\sqrt 2} * \frac{\sqrt 2}{\sqrt 2}$

$cos\ \varnothing = \frac{-7*\sqrt 2}{5*2}$

$cos\ \varnothing = \frac{-7\sqrt 2}{10}$

$cos\ \varnothing = \frac{-7}{10}\sqrt 2$

$tan\ \varnothing = \frac{y}{x}$

$tan\ \varnothing = \frac{-1}{-7}$

$tan\ \varnothing = \frac{1}{7}$

$cot\ \varnothing = \frac{x}{y}$

$cot\ \varnothing = \frac{-7}{-1}$

$cot\ \varnothing = 7$

$sec\ \varnothing = \frac{r}{x}$

$sec\ \varnothing = \frac{5\sqrt 2}{-7}$

$sec\ \varnothing = \frac{-5}{7}\sqrt 2$

$csc\ \varnothing = \frac{r}{y}$

$csc\ \varnothing = \frac{5\sqrt 2}{-1}$

$csc\ \varnothing = -5\sqrt 2$

3 0

3 years ago

PLEASE HELP ASAP!!! I NEED CORRECT ANSWERS ONLY PLEASE!!!

aleksley [76]

The length of PR is 4.4 units.

Explanation:

It is given that the length of the hypotenuse is 10 units.

Also, the angle of R is 64°

To find the length of PR, we shall use the cosine formula,

$\cos \theta=\frac{a d j}{h y p}$

Here, $\theta=64$ , adj = PR and hyp = 10

Substituting these values in the formula, we get,

$\cos 64=\frac{P R}{10}$

Multiplying both sides by 10, we get,

$10*\cos 64={P R}$

Substituting the value for cos 64, we get,

$10*0.438={P R}$

Multiplying, we have,

$4.38=PR$

Rounding off, we get,

$PR=4.4$

Thus, the length of PR is 4.4 units.

8 0

3 years ago

An angle, θ, is in standard position. The terminal side of the angle passes through the point (4, 5).

lara31 [8.8K]

Answer:

cos Θ = $\frac{4}{\sqrt{41} }$

Step-by-step explanation:

Given the angle passes through (4, 5 ) then the right triangle with sides 4 and 5 has hypotenuse h given by

h² = 4² + 5² = 16 + 25 = 41 ( take the square root of both sides )

h = $\sqrt{41}$

In relation to Θ, 4 is adjacent and 5 is opposite, thus

cos Θ = $\frac{adjacent}{hypotenuse}$ = $\frac{4}{\sqrt{41} }$

5 0

3 years ago

4a-b<br> Evaluate the expression when a=5 and b=-7

stepladder [879]

Answer:

27

Step-by-step explanation:

So first we need to plug in 5 as the variable a and -7 as the variable b

4(5)-(-7)

Next we multiply the 4 and the 5 together to get 20

4(5) = 20 or 4 x 5 = 20

20-(-7)

Now we subtract negative 7 from 20

20-(-7) = 27

This can also be written as 20 plus 7 as a mathematical rule states: two negatives make a positive. So:

20-(-7) = 20 + 7

Both of these are equivalent in every sense of the word and give us our final answer of 27

8 0

3 years ago

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