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vlabodo [156]
3 years ago
9

Can you answer questions 71, and 72?

Mathematics
1 answer:
antiseptic1488 [7]3 years ago
6 0
I think 71 is B
and 72 is D.

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Find the exact value of sin(cos^-1(4/5))
boyakko [2]
If you're using the app, try seeing this answer through your browser:  brainly.com/question/2762144

_______________


Let  \mathsf{\theta=cos^{-1}\!\left(\dfrac{4}{5}\right).}


\mathsf{0\le \theta\le\pi,}  because that is the range of the inverse cosine funcition.


Also,

\mathsf{cos\,\theta=cos\!\left[cos^{-1}\!\left(\dfrac{4}{5}\right)\right]}\\\\\\
\mathsf{cos\,\theta=\dfrac{4}{5}}\\\\\\ \mathsf{5\,cos\,\theta=4}


Square both sides and apply the fundamental trigonometric identity:

\mathsf{(5\,cos\,\theta)^2=4^2}\\\\
\mathsf{5^2\,cos^2\,\theta=4^2}\\\\
\mathsf{25\,cos^2\,\theta=16\qquad\qquad(but,~cos^2\,\theta=1-sin^2\,\theta)}\\\\
\mathsf{25\cdot (1-sin^2\,\theta)=16}

\mathsf{25-25\,sin^2\,\theta=16}\\\\
\mathsf{25-16=25\,sin^2\,\theta}\\\\
\mathsf{9=25\,sin^2\,\theta}\\\\
\mathsf{sin^2\,\theta=\dfrac{9}{25}}


\mathsf{sin\,\theta=\pm\,\sqrt{\dfrac{9}{25}}}\\\\\\
\mathsf{sin\,\theta=\pm\,\sqrt{\dfrac{3^2}{5^2}}}\\\\\\
\mathsf{sin\,\theta=\pm\,\dfrac{3}{5}}


But \mathsf{0\le \theta\le\pi,} which means \theta lies either in the 1st or the 2nd quadrant. So \mathsf{sin\,\theta} is a positive number:

\mathsf{sin\,\theta=\dfrac{3}{5}}\\\\\\
\therefore~~\mathsf{sin\!\left[cos^{-1}\!\left(\dfrac{4}{5}\right)\right]=\dfrac{3}{5}\qquad\quad\checkmark}


I hope this helps. =)


Tags:  <em>inverse trigonometric function cosine sine cos sin trig trigonometry</em>

3 0
3 years ago
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tangare [24]

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Step-by-step explanation:

IM NOT SURE I THINK BUT hope this helps :)

7 0
3 years ago
2 + yx; use x = 6, and y = 5
Brrunno [24]

Answer:

answer: 32

Step-by-step explanation:

2+5*6

=32

4 0
3 years ago
Theo earned £15400 last year and spent 6% of his money on making home improvements. Find how much money Theo spent on home impro
inn [45]

Answer:

15400 ÷ 6/100

Step-by-step explanation:

next step do yourself

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5 0
2 years ago
A copy machine can make 742 copies in 53 minutes. How many copies can the machine make in 1 minute?
olasank [31]

Answer:

14 copies per minute

Step-by-step explanation:

Take 742 copies and divide by 53 minutes

742/53 =14

14 copies per minute

6 0
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