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notka56 [123]
2 years ago
10

Use a double angle or half angle identity to find the exact value of each expression

Mathematics
1 answer:
STatiana [176]2 years ago
4 0

Answer:

Step-by-step explanation:

There are 2 very distinct and important things that we need to know before completing the problem. First is that we are given that the cos of an angle is 1/3 (adjacent/hypotenuse) and it is in the first quadrant. We also need to know that the identity for sin2θ = 2sinθcosθ.

We already know cos θ = 1/3, so we need now find the sin θ. The sin ratio is the side opposite the angle over the hypotenuse, and the side we are missing is the side opposite the angle (we do not need to know the angle; it's irrelevant). Set up a right triangle in the first quadrant and label the base with a 1 (because the base is the side adjacent to the angle), and the hypotenuse with a 3. Find the third side using Pythagorean's Theorem:

3^2=1^2+y^2 which simplifies to

9=1+y^2 and

y^2=8 so

y=\sqrt{8}=2\sqrt{2} so that's the missing side. Now we can easily determine that

sin\theta=\frac{2\sqrt{2} }{3}

Now we have everything we need to fill in the identity for sin2θ:

2sin\theta cos\theta=2(\frac{2\sqrt{2} }{3})(\frac{1}{3}) and multiply all of that together to get

2sin\theta cos\theta=\frac{4\sqrt{2} }{9}

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Answer: D

<u>Step-by-step explanation:</u>

The first matrix contains the coefficients of the x- and y- values for both equations (top row is the top equation and the bottom row is the bottom equation. The second matrix contains what each equation is equal to.

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The product will result in the solution for the x- and y-values of the system.

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Step-by-step explanation:

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Here, we want to find out which of the functions is required to determine the number of lunches L prepared after m minutes

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Mathematically, that would be;

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