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3 years ago

13

Write an algebraic rule for the rotation for s (-1,3) s' (-3,-1)

1 answer:

USPshnik [31]3 years ago

6 0

That's the symmetric property

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Solve questions 15,16,17, and 18. Will give Brainliest!! Please!!! Show minimal work!

SVEN [57.7K]

15. The terminal side of $\frac{3\pi}{2}$ intercepted the unit circle at:

(0,-1).

This implies that:

$(\cos \frac{3\pi}{2}, \sin \frac{3\pi}{2}=(0,-1)$

This implies that:

$\cos \frac{3\pi}{2}=0,\:and\: \sin \frac{3\pi}{2}=-1$

16) We have that: $\cot \theta =-\frac{6}{7}$ .

We illustrate this on the right triangle and apply the Pythagoras Theorem as follows:

$h^2=6^2+7^2$

$h^2=36+49$

$h^2=85$

$h=\sqrt{85}$

Using the mnemonics SOH-CAH-TOAH, we have:

$\sin \theta=-\frac{Opp}{Hyp}=-\frac{7}{\sqrt{85} }=-\frac{7\sqrt{85} }{85}$

$\cos \theta=\frac{Adj}{Hyp}=\frac{6}{\sqrt{85} }=\frac{6\sqrt{85} }{85}$

$\tan \theta=-\frac{Opp}{Adj}=-\frac{7}{6}}$

$\csc \theta=-\frac{Hyp}{Opp}=-\frac{\sqrt{85} }{7}$

$\sec \theta=\frac{Hyp}{Adj}=\frac{\sqrt{85} }{6}$

17. We want to verify that: $sin^4x-sin^2x=cos^4x-cos^2x$

Verifying from the LHS

$\sin^4x-sin^2x=(sin^2x)^2-sin^2x$

Recall that from the Pythagorean identity: $\sin^2x=1-\cos^2x$

$\sin^4x-sin^2x=(1-cos^2x)^2-(1-\cos^2x)$

$\sin^4x-sin^2x=1-2cos^2x+\cos^4x-1+\cos^2x$

$\sin^4x-sin^2x=\cos^4x-\cos^2x$

18. We have:

$\tan^2x\sec^2x+2\sec^2x-\tan^2x=2$

$\tan^2x\sec^2x+2\sec^2x-\tan^2x-2=0$

$\sec^2x(\tan^2x+2)-1(\tan^2x+2)=0$

$(\sec^2x-1)(\tan^2x+2)=0$

When $(\sec^2x-1)=0$ , we have

$x=0,\pi$

When $\tan^2x+2=0$ , $\tan^2x=-2$

We can see this is not defined for all real values of x.

6 0

3 years ago

Question 4 (4 points

aalyn [17]

Answer:

It is True 200% legit!

Step-by-step explanation:

4 0

3 years ago

1/6x -5/9xy^2<br> Find the least common denominator for the two expressions.

eimsori [14]

Answer:

Step-by-step explanation:

6x=2×3×x

9xy²=3×3×x×y²

common denominator=2×3×3×x×y²=18xy²

4 0

4 years ago

In the following diagram,

olga2289 [7]

Answer:

x + 75 = 180, as these two angles form a straight angle.
x = 180° - 75° = 105°

<u>y and x are supplementary angles as p is transversal of l and m:</u>

y + x = 180°
y = 180° - x = 180° - 105° = 75°

<u>z is same as 86° as vertical angles:</u>

z = 86°

<u>w and z are supplementary angles as g is transversal of l and m:</u>

w + z = 180°
w = 180° - z = 180° - 86° = 94°

6 0

3 years ago

Juno calculated the area of a square to be 4/9 square yard. Which shows the side length of the square?

Stella [2.4K]

$\bf \textit{area of a square}\\\\
A=s^2~~
\begin{cases}
s=side's~length\\
--------\\
A=\frac{4}{9}
\end{cases}\implies \cfrac{4}{9}=s^2
\\\\\\
\sqrt{\cfrac{4}{9}}=s\implies \cfrac{\sqrt{4}}{\sqrt{9}}=s\implies \cfrac{2}{3}=s$

3 0

3 years ago