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zimovet [89]
3 years ago
9

Given cosθ=5/6 and θ lies in Quadrant I .

Mathematics
2 answers:
Julli [10]3 years ago
6 0
With this, we know cos=x/r

x = 5
and
r = 6

We need to find y.

25 + y² = 36

y² = 11

y = √11

sin of theta would be √11/6
Ymorist [56]3 years ago
5 0

Answer: The answer is \dfrac{\sqrt 11}{6}.

Step-by-step explanation:  Given that \cos \theta=\dfrac{5}{6} and \theta lies in the first quadrant. We are to find the exact value of \sin \theta in simplified form.

We know that

\sin^2\theta+\cos^2\theta=1\\\\\Rightarrow \sin \theta=\pm\sqrt{1-\cos^2\theta}.

Since sine of an angle is positive in the 1st quadrant, so we have

\sin \theta=\sqrt{1-\cos^2\theta}=\sqrt{1-\dfrac{25}{36}}=\sqrt{\dfrac{11}{36}}=\dfrac{\sqrt{11}}{6}.

Thus, the answer is \dfrac{\sqrt{11}}{6}.

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Answer:

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3) the answer is No, proof:  √-1 - 3 is not defined because √-1 doesn't exist

4) the answer is Yes, proof: (√-1 )²=  -1 this is a real number

5) the answer is No, proof:  (√-1 )^3=  (√-1 )²(√-1 )= - 1(√-1 ), and - 1(√-1 ) is not defined because √-1 doesn't exist

6) the result would be defined with the following cases:

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7) the result would not be defined with the following cases:

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 i²= -1, it implies i= √-1

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Step-by-step explanation:

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