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Elza [17]
4 years ago
10

The terminal side of angle θ intersects the unit circle in the first quadrant at (925,y). What are the exact values of sinθ and

cosθ?
Mathematics
1 answer:
Nonamiya [84]4 years ago
8 0

Correct question is;

The terminal side of angle θ intersects the unit circle in the first quadrant at (9/25,y). What are the exact values of sinθ and cosθ?

Answer:

sinθ = (√544)/25) and cosθ = 9/25

Step-by-step explanation:

We are given that (9/25,y) lies on the unit circle. Thus, from general representation of equation of a circle, we can write that;

(9/25)² + y² = 1²

y² = 1 - (9/25)²

y² = (625 - 81)/25²

y² = 544/25²

y = ±(√544)/25

We are told the point is in the first quadrant and so we will choose the positive value of y = (√544)/25.

Therefore, the terminal side of the angle θ intersects the unit circle at [9/25, (√544)/25)]

In unit circle geometry, cosθ = x, while sinθ = y.

Thus; sinθ = (√544)/25) and cosθ = 9/25

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Squared of the sum of the differences = (9-6.4)^2 + (7-6.4)^2 + (6.5-6.4)^2 + (7.5-6.4)^2 + (7-6.4)^2 + (8-6.4)^2 + (5-6.4)^2 + (6-6.4)^2 + (7.5-6.4)^2 + (8-6.4)^2 = 17.15

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A child builds two wooden train sets. The path of one of the trains can be represented by the function y = 2cos2x, where y repre
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Using a trigonometric equation, it is found that it will take 2.28 minutes until the two trains are first equidistant from the child.

<h3>What is the distance of each train to the child?</h3>

The distance of the first train is:

y_1 = 2\cos^{2}x

The distance of the second train is:

y_2 = 3 + \cos{x}

<h3>When are the trains equidistant to the child?</h3>

When y_1 = y_2, hence:

2\cos^{2}x = 3 + \cos{x}

The following substitution is made:

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Which is a quadratic equation with coefficients a = 2, b = -1, c = -3, hence:

\Delta = b^2 - 4ac = (-1)^2 - 4(1)(-3) = 13

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You can learn more about trigonometric equations at brainly.com/question/2088730

8 0
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7 0
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