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3 years ago

If tan(theta) is 5/12 and theta is an acute angle, find sin(theta)

Mathematics

1 answer:

navik [9.2K]3 years ago

7 0

Comment

The tangent represents the sides making up the right angle in a right angle triangle. To find out the answer to what you have asked, the simplest way is to assume that you are talking about a right angle triangle.

Step One

Find the hypotenuse. Use a variation of the Pythagorean Theorem.

opposite^2 + adjacent^2 = hypotenuse^2

5^2 + 12^2 = x^2

25 + 144 = x^2

x^2 = 169

sqrt(x^2) = sqrt(169)

x = 13

Step Two

Find the sine.

When the tangent is given, the opposite in this case is 5.

That's because the opposite is always the numerator of a tangent.

Sin(theta) = 5/13 Answer

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6 0

3 years ago

Multiply:4x^3sqrt4x^2(2^3sqrt32x^2-x^3sqrt2x)

larisa [96]

8x^5\left(32\sqrt{2}x^2-\sqrt{2}x^4\right)

7 0

3 years ago

Read 2 more answers

Y=-x^2+6x-4 Find the Axis of Symmetry and the Vertex, Also solve the whole equation.

Inessa [10]

Answer:

1. Axis of symmetry: x = 3

2. Vertex: (3,5)

3. Solution of the equation:

x-intercepts:

$(3-\sqrt{5},0) \\\\(3+\sqrt{5},0)$

y-intercept: (0, -4)

Explanation:

1. Equation:

$y=-x^2+6x-4$

2. Axis of symmetry:

That is the equation of a parabola, whose standard form is:

$y=ax^2+bx+c$

Where:

$a=-1;b=6;c=-4$

The axis of symmetry is the vertical line with equation:

$x=-b/2a$

Substitute $a=-1,\text{ and }b=6$

$x=-6/[(2)(-1)]=-6/(-2)=3$

Thus, the axis of symmetry is:

$x=3$

3. Vertex

The x-coordinate of the vertex is equal to the axys of symmetry, i.e x = 3.

To find the y-xoordinate, substitute this value of x into the equation for y:

$y=-x^2+6x-4\\\\y=-(3)^2+6(3)-4=-9+18-4=5$

Therefore, the vertex is (3, 5)

4. Find the x-intercepts

The x-intercepts are the roots of the equation, which are the points wher y = 0.

$y=-x^2+6x-4=0$

Use the quadratic equation:

$x=\frac{-b\pm \sqrt{b^2-4ac} }{2a} \\\\x=\frac{-6\pm\sqrt{(-6)^2-4(-1)(-4)} }{2(-1)}\\\\x_1=3-\sqrt{5} \\\\x_2=3+\sqrt{5}$

5. Find the y-intercept

The y-intercet is the value of y when x=0:

$y=-x^2+6x-4\\\\y=-(0)^2+6(0)-4=-4$

7 0

4 years ago

Which of these examples is an error of addition by one?

N76 [4]

Answer:

The correct answer is:

A. 27,465 +52,534 = 79,899

Step-by-step explanation:

Given are the options for addition

We have to check each addition one by one

So,

A. 27,465 +52,534 = 79,899

This option is the example of error of addition by one. The answer should have been 79,999. Hence there is an error in addition ..

Hence, option a: 27,465 +52,534 = 79,899 is the correct answer ..

4 0

3 years ago

Read 2 more answers

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Anestetic [448]

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and multyplied :you sum up them

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m^5*m^-7=m^5-7=m^-2

8 0

3 years ago