To do this, we must use the unit circle. At the angle $\frac{\pi }{6}$ the coordinate pair is ( $\frac{\sqrt{3} }{2}$ , $\frac{1}{2}$ ) and the hypotenuse is 1

Now that we know these we can start using the trig functions

sin = y

cos = x

tan = $\frac{y}{x}$

And the other functions would be the reciprocal of these

csc = $\frac{1}{y}$

sec = $\frac{1}{x}$

cot = $\frac{x}{y}$

This would mean that

sinx = $\frac{1}{2}$

cosx = $\frac{\sqrt{3} }{2}$

tanx = $\frac{1}{\sqrt{3} }$ or $\frac{\sqrt{3} }{3}$ if you're supposed to rationalize your denominators

cscx = 2

secx = $\frac{2}{\sqrt{3} }$ or $\frac{2\sqrt{3} }{3}$

cot = $\sqrt{3}$

6 0

2 years ago

Adante begins to evaluate the expression 3 1/3 * 5 1/4

goldenfox [79]

For this case we must find the product of two mixed numbers:

$3 \frac {1} {3} = 3 + \frac {1} {3} = \frac {9 + 1} {3} = \frac {10} {3}\\5 \frac {1} {4} = 5 + \frac {1} {4} = \frac {20 + 1} {4} = \frac {21} {4}$

So, we have:

$\frac {10} {3} * \frac {21} {4} = \frac {10 * 21} {3 * 4} = \frac {210} {12} = \frac {105} {6} = \frac {35} {2}$

If we go to a mixed number we have:

$\frac {35} {2} = 17 \frac {1} {2}$

Answer:

$17 \frac {1} {2}$

4 0

3 years ago

Given the equation 5x − 4 = –2(3x + 2), solve for the variable. Explain each step and justify your process.

blagie [28]

A.
$5x-4=-2(3x+2) \ \ \ \ \ \ \ \ \ |\hbox{expand the bracket} \\
5x-4=-2 \times 3x-2 \times 2 \\
5x-4=-6x-4 \ \ \ \ \ \ \ \ \ \ \ \ \ |\hbox{add 6x to both sides} \\
11x-4=-4 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ |\hbox{add 4 to both sides} \\
11x=0 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ |\hbox{divide both sides by 11} \\
x=0$

B.
$3(2x-4)=5x-1 \\
6x-12=5x-1 \\
\boxed{11x-12=-1} \Leftarrow \hbox{the first mistake} \\
11x=11 \\
\boxed{x=11} \Leftarrow \hbox{the second mistake}$

Megan's solution isn't correct.
The first mistake: she subtracted 5x from the right-hand side of the equation, but added 5x to the left-hand side.
The second mistake: she divided the right-hand side of the equation by 11, but didn't divide the left-hand side.

The correct solution:
$3(2x-4)=5x-1 \ \ \ \ \ \ \ \ \ \ \ |\hbox{expand the bracket} \\
3 \times 2x+3 \times (-4)=5x-1 \\ 6x-12=5x-1 \ \ \ \ \ \ \ \ \ \ \ \ \ \ |\hbox{subtract 5x from both sides} \\
x-12=-1 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ |\hbox{add 12 to both sides} \\
x=11$

3 0

2 years ago

Andrew has one book that is two and 378 inches thick and a second book that is 3.56 inches thick if he stacks the books about ho

Georgia [21]

2.378 + 3.56 = 5.938

two and 378 inches = 2.378

8 0

3 years ago