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2 years ago

Suppose cos(O) = 5/13, Quadrant I. Find sin(O). A:13/12 B:12/13 C:13/5 D:5/12

Mathematics

1 answer:

Ne4ueva [31]2 years ago

8 0

Answer:

B. 12/13.

Step-by-step explanation:

Using the identity sin^2 O + cos^2 O = 1:

sin^2 O = 1 - cos^2 O

sin^2 O = 1 - (5/13)^2

= 1 - 25/169

= 169/169 - 25/169

= 144/169

So sin O = √(144/169)

= 12/13.

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compute the projection of → a onto → b and the vector component of → a orthogonal to → b . give exact answers.

Nina [5.8K]

$\text { Saclar projection } \frac{1}{\sqrt{3}} \text { and Vector projection } \frac{1}{3}(\hat{i}+\hat{j}+\hat{k})$

We have been given two vectors $\vec{a}$ and $\vec{b}$ , we are to find out the scalar and vector projection of $\vec{b}$ onto $\vec{a}$

we have $\vec{a}=\hat{i}+\hat{j}+\hat{k}$ and $\vec{b}=\hat{i}-\hat{j}+\hat{k}$

The scalar projection of $\vec{b}$ onto $\vec{a}$ means the magnitude of the resolved component of $\vec{b}$ the direction of $\vec{a}$ and is given by

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$\begin{aligned}&=\frac{(\hat{i}+\hat{j}+\hat{k}) \cdot(\hat{i}-\hat{j}+\hat{k})}{\sqrt{1^2+1^1+1^2}} \\&=\frac{1^2-1^2+1^2}{\sqrt{3}}=\frac{1}{\sqrt{3}}\end{aligned}$

The Vector projection of $\vec{b}$ onto $\vec{a}$ means the resolved component of $\vec{b}$ in the direction of $\vec{a}$ and is given by

The vector projection of $\vec{b}$ onto

$\vec{a}=\frac{\vec{b} \cdot \vec{a}}{|\vec{a}|^2} \cdot(\hat{i}+\hat{j}+\hat{k})$

$\begin{aligned}&=\frac{(\hat{i}+\hat{j}+\hat{k}) \cdot(\hat{i}-\hat{j}+\hat{k})}{\left(\sqrt{1^2+1^1+1^2}\right)^2} \cdot(\hat{i}+\hat{j}+\hat{k}) \\&=\frac{1^2-1^2+1^2}{3} \cdot(\hat{i}+\hat{j}+\hat{k})=\frac{1}{3}(\hat{i}+\hat{j}+\hat{k})\end{aligned}$

To learn more about scalar and vector projection visit:brainly.com/question/21925479

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1 year ago

The radius of a circle is 9 feet. What is the circumference?

Vlad1618 [11]

Answer: 18 $\pi$

Step-by-step explanation:

The circumference formula is C= 2 $\pi$ r

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3 years ago

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$\bf n^{th}\textit{ term of a geometric sequence}\\\\
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3 years ago

Four times the sum of a number and ter is the same as one-hundred added to eight

AfilCa [17]

Answer:

GIVE BRAINLIEST PLZ

I DONT NEED THNX

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1) Four times sum of a number and 10

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-15 = x

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