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murzikaleks [220]
2 years ago
14

Find values of  that satisfy the equation for 0º    360º and 0  θ  2 . Give answers in degrees and radians.

Mathematics
1 answer:
suter [353]2 years ago
8 0

Answer:

\theta = 30^\circ, 330^\circ

\theta = \frac{\pi}{6}, \frac{11\pi}{6}

Step-by-step explanation:

Given [Missing from the question]

Equation:

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

Interval:

0 \le \theta \le 360

0 \le \theta \le 2\pi

Required

Determine the values of \theta

The given expression:

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

... shows that the value of \theta is positive

The cosine of an angle has positive values in the first and the fourth quadrants.

So, we have:

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

Take arccos of both sides

\theta = cos^{-1}(\frac{\sqrt 3}{2})

\theta = 30 --- In the first quadrant

In the fourth quadrant, the value is:

\theta = 360 -30

\theta = 330

So, the values of \theta in degrees are:

\theta = 30^\circ, 330^\circ

Convert to radians (Multiply both angles by \pi/180)

So, we have:

\theta = \frac{30 * \pi}{180}, \frac{330 * \pi}{180}

\theta = \frac{\pi}{6}, \frac{33 * \pi}{18}

\theta = \frac{\pi}{6}, \frac{11 * \pi}{6}

\theta = \frac{\pi}{6}, \frac{11\pi}{6}

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Answer:

It's 39/89

Step-by-step explanation:

cos X = adjacent/ hypotenuse = 39/89

6 0
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Which set of angles could be the interior angles of a triangle? O A. 10° 20°, and 60° B. 20°. 20°, and 50° C. 209.30'. and 50° D
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7 0
3 years ago
What are the exact solutions of x2 − 5x − 7 = 0, where x equals negative b plus or minus the square root of b squared minus 4 ti
Marat540 [252]

Answer:

x = \frac{5 + \sqrt{53}}{2}  or  x = \frac{5 - \sqrt{53}}{2}

Step-by-step explanation:

Given

x^2 - 5x - 7 = 0

Required

Solve for x using:

x = \frac{-b \± \sqrt{b^2 - 4ac}}{2a}

First, we need to identify a, b and c

The general form of a quadratic equation is:

ax^2 + bx + c = 0

So, by comparison with x^2 - 5x - 7 = 0

a = 1     b = -5      c = -7

Substitute these values of a, b and c in

x = \frac{-b \± \sqrt{b^2 - 4ac}}{2a}

x = \frac{-(-5) \± \sqrt{(-5)^2 - 4 * 1 * -7}}{2 * 1}

x = \frac{5 \± \sqrt{25 +28}}{2}

x = \frac{5 \± \sqrt{53}}{2}

Split the expression to two

x = \frac{5 + \sqrt{53}}{2}  or  x = \frac{5 - \sqrt{53}}{2}

To solve further in decimal form, we have

x = \frac{5 + 7.28}{2}  or  x = \frac{5 - 7.28}{2}

x = \frac{12.28}{2}  or  x = \frac{-2.28}{2}

x = 6.14 or x = -1.14

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3 years ago
What is the coefficient of xy^2<br> in the expansion of (x+y)^3?
Basile [38]

Step-by-step explanation:

Using Binomial Expansion,

(x + y)³

= 3C0 * x³ + 3C1 * x²y + 3C2 * xy² + 3C3 * y³.

Therefore the coefficient of xy² is 3C2 = 3.

5 0
3 years ago
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Your answer is5x^4 * sqrt 3x
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