AzizHusain

cos(17pi/6)

We know that pi/6 = 30 degrees, so 17pi/6 must be 30*17 = 510 degrees.

Also, note that pi = 180 degrees which means 2pi = 360 degrees.

Now, 510 - 360 degrees = 150 degrees, which means we have made a full 2pi revolution and are left with 150 degrees --> which is pi/6*5 [30 degrees*5 = 150 degrees] --> 5pi/6.

Now, cos(5pi/6) can be evaluated as 150 degrees or the 2nd quadrant with a negative x value since pi/6 is positive sqrt3/2 and lies in the 1st quadrant.

Therefore, we have cos(5pi/6) = -sqrt(3)/2.

46.2*10^-2 --> You have to move the decimal place to the left twice (since it is ^-2) instead of right twice, so the answer will be 0.462.

2x^2+3cy-4y^2; x = 2 & y = -4

2(2^2) + 3c(-4) - 4(-4^2) -->

8 -12c - 64 --> 

We need to know: c = ?

DS, remember the order of operations - pemdas --> multiplication before addition

10/sin(50 degrees) = 13.0540728933224117.

9^x = 27^x+1

Rewrite: 3^2x = 3^3(x+1) -->

2x = 3(x+1) -->

2x = 3x + 3 -->

-3 = x --> 

x = -3.

3/4 of 2728 = 0.75*2728 = 2,046 --> 2,046 of the addresses on that list will be incorrect.

4 quarters + 3 dimes + 2 nickels + 2 pennies = 11 coins total

We are interested in finding out how much of the collection is dimes only --> 3 dimes / 11 total = 3/11.

sin(pi/6)*cosx - cos(pi/6)*sinx = -1/2; interval [0, 2pi]

Using the unit circle, we know that sin(pi/6) = 1/2 & cos(pi/6) = sqrt(3)/2 -->

1/2*cosx - sqrt(3)/2*sinx = -1/2

If x = pi/2 --> 1/2*cos(pi/2) - sqrt(3)/2*sin(pi/2) = 0 - sqrt(3)/2*1 = 0 - sqrt(3)/2 = -sqrt(3)/2

If x = pi/3 --> 1/2*cos(pi/3) - sqrt(3)/2*sin(pi/3) = 1/2*(1/2) - sqrt(3)/2*sqrt(3)/2 = 1/4 - 3/4 = -2/4 = -1/2

If x = pi/4 --> 1/2*cos(pi/4) - sqrt(3)/2*sin(pi/4) = 1/2*(sqrt(2)/2) - sqrt(3)/2*(sqrt(2)/2) = sqrt2/4 - sqrt6/4 = [sqrt(2) - sqrt(6)] / 4 = -0.259

If x = pi --> 1/2*cos(pi) - sqrt(3)/2*sin(pi) = 1/2*(-1) - sqrt(3)/2*0 = -1/2

If x = 2pi --> 1/2*cos(2pi) - sqrt(3)/2*sin(2pi) = 1/2*(1) - sqrt(3)/2*0 = 1/2

Note: We have x = pi/3 & x = pi so far, but we can also consider 2pi/3, 4pi/3, etc.

If x = 2pi/3, we notice that we would get -1/4 - sqrt(3)/2*sqrt(3)/2 = -1/4 - 3/4 = -4/4 = 1

If x = 4pi/3, -1/4 - sqrt(3)/2*-sqrt(3)/2 = -1/4 + 3/4 = 2/4 = 1/2

If x = 5pi/3, 1/4 - sqrt(3)/2*-sqrt(3)/2 = 1/4 + 3/4 = 4/4 = 1.

So, x = pi/3 & x = pi satisfy the equation.

Use the "log" or the "ln" key when you want to find the log of something and for anti-logs, use the 10^x key.

if y = log(3) [assume base of 10] --> y= 0.4771212547196624.

The anti-log would be 10^3 = 1,000.

if f(x) = f(-x), then the function is even. So, f(-x) = 2^-x which does not equal 2^x.

However, if f(-x) = -f(x), then the function is odd. So -f(x) = -2^x which does not equal f(-x) = 2^-x.

f(x) = 2^x is neither even nor odd.