First we need to set this ratio up in the coordinate plane. Because this is tangent, the 3 goes opposite the reference angle and the 4 goes along the x-axis, adjacent to the reference angle. We see that we are missing the third side of the triangle when we do this, namely the hypotenuse. We use Pythagorean's Theorem to find that this side is 5. Now we have to deal with the identities for each sin(2A) and cos(2A).

sin(2A) = 2sin(A)cos(A)

We know from the triangle we drew in the coordinate plane that

$sin(A)=\frac{3}{5}$ and $cos(A)=\frac{4}{5}$ so we fill in the formula accordingly and then simplify:

$sin(2A)=2(\frac{3}{5})(\frac{4}{5})=\frac{24}{25}$

cos(2A) has 3 identities; I just picked the one I thought would be easiest to use and went with that one. Regardless of which one you pick you will get the same answer as long as you do the math correctly.

$cos(2A)=cos^2(A)-sin^2(A)$ and filling in the formula:

$cos(2A)=(\frac{4}{5})^2-(\frac{3}{5})^2\\cos(2A)=\frac{16}{25}-\frac{9}{25}\\cos(2A)=\frac{7}{25}$

I'm not sure why you have 7/2 there...

8 0

3 years ago

Reena has 12 more dimes than she does quarters. If Reena has a total of 28 coins, how many quarters, qq, and how many dimes, dd,

erastovalidia [21]

Q = d - 12
q = 28 - d

d - 12 = 28 - d
d + d = 28 + 12
2d = 40
d = 40/2
d = 20 <== 20 dimes

q = d - 12
q = 20 - 12
q = 8 <== 8 quarters

5 0

4 years ago

Write an equation of the line passing through (-5,5) and having slope -6. Guve the answer in slope-intercept form.

Fynjy0 [20]

Passes through (-5, 5) & has a slope of -6.

We want the answer in slope-intercept form.

** Remember! Slope-intercept form : y=mx+b where m=slope, b=y-intercept.

Simply plug everything in :)

y = mx + b

y = (-6)x + (5)

Simplify.

y = -6x + 5

~Hope I helped!~

8 0

4 years ago