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mars1129 [50]
3 years ago
7

Is the sqrt of 1 - sin^2 theta = cos theta true? If so, in which quadrants does angle theta terminate?

Mathematics
1 answer:
Genrish500 [490]3 years ago
7 0

Answer:

Answer: The answer is option B.

Step-by-step explanation:

Here,

We have,

{ \sin }^{2}  theta \: +  {cos}^{2}theta  = 1

{cos}^{2} \: theta  = 1 -  {sin}^{2}  \: theta

cos \: theta =  \sqrt{1 -  { \sin }^{2}theta }

So, it's true; and it lies in quadrant 1 and 4.

The reason according to the "CAST" rule cos theta is in 1st and 3rd quadrant cos theta is positive.

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Check all of the ordered pairs that satisfy the equation below.y=2/5x
zvonat [6]

We are going to do this step by step:

Let's start with option A

A.

X = 25 and Y = 5/2

y=\frac{2}{5}\cdot x=\frac{2}{5}\cdot25=\frac{2\cdot25}{5}=\frac{50}{5}=\frac{5\cdot10}{5\cdot1}=10

In this case, when X = 25 , then Y = 10 ,which is different to 5/2

B.

X = 14 , Y = 35

y=\frac{2}{5}\cdot14=\frac{28}{5}

In case, when X = 14, then Y = 28/5, which is different to 35

C.

X = 40 , Y = 24

y=\frac{2}{5}\cdot40=\frac{80}{5}=16

Similarly, in this case, when X = 40, then Y = 16, which is different to 24

D.

X = 10 , Y=4

y=\frac{2}{5}\cdot10=\frac{20}{5}=4

Now, in this case, we can see that when X = 10, then Y = 4 which is the same as the given value of Y

E.

X = 50 , Y = 20

y=\frac{2}{5}\cdot50=\frac{100}{5}=20

In this case, the values of Y are also the same.

F.

X = 30 , Y = 12

y=\frac{2}{5}\cdot30=\frac{60}{5}=12

Again, in this case, the values of Y are the same, so the pair satisfies the equation.

In conclusion: options D, E and F satisfy the equation

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11 months ago
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Luba_88 [7]
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