Trigonometry

1

cos(t) = 0.92568

therefore t = cos-1(0.92568) = 0.3880.

If the answer comes out as 22.23, the calculator is set to degrees. Simply multiply that result by pi/180 to convert to radians (or reset the calculator to work in radians). Excel, for example, works in radians.

From that primary value you get

t = 0.3880 + 2*k*pi

and

t = 2*k*pi - 0.3880

for all integer values of k.

The result is a direct consequence of the sine rule.

- 0.5 sqrt(3) = - 0.866 (rounded)

sine[theta]=opposite/hypotenuse=square root of (1-[cos[theta]]^2)

tan = sin/cos

Now cos2 = 1 - sin2 so cos = +/- sqrt(1 - sin2)

In the second quadrant, cos is negative, so cos = - sqrt(1 - sin2)

So that tan = sin/[-sqrt(1 - sin2)]

or -sin/sqrt(1 - sin2)

For navigational purposes

cot(45 deg) = 1.

degree x 1rev/360degree

opposite/hypotenuse

How do you solve ln|tan(x)|=ln|sin(x)|-ln|cos(x)|? Well you start by........

It means that you have so many choices to go by.

∫ cos(x) dx

= -sin(x) + C

Yes, an Octahedron has 8 faces. But how many edges? Let's see, 4 on top, 4 on bottom and 4 connectors. I think that would be a total of 12.

(x^2 + 9x +14) / (x+5)

Factor (x^2 + 9x +14)

[(x+7)(x+2)]/[(x+5)], x cannot equal -5

alien planet

A=pi*r^2, so to find the radius, divide the area by pi and take the square root of that quotient. theta/360=arc length/circumference. C=2pi*r, so multiply the radius you found above by 2pi. Then you have theta/(known value)=(known value)/(known value), so you can now solve for theta!

Draw a right triangle. To get a tangent of 2, the side opposite the angle might be 2, the adjacent side might be 1 (other combinations, in the ratio 2:1, are also possible). In this case, the hypothenuse is square root of 5 (Law of Pythagoras). Therefore, the cosine is 1 / square root of 5.

Use the sine ratio to find the height of the kite:

sine = opposite (height of kite with the horizontal) divided by the hypotenuse (the string)

Rearrange the formula:

sine*hypotenuse = opposite

sine 25 degrees*150 = 63.39273926 feet

Height of kite above the ground: 63.39273926+4.5 = 67.89273926 feet

Therefore the kite is 68 feet above the ground to the nearest foot

It is -pi/4 radians = -45 deg.

cos(15 deg) = 0.9659, approx.

99-100 cm

The solutions are (4n - 1)*pi/2 for all integer values of n.

If you are looking for the angle of elevation from the ground to the top of Qutub Minar, here is a solution. Qutub Minar is 72.5 meters tall. The angle of elevation would equal arctan(72.5/5). It comes out to approximately 86.05 degrees.

Nitrogen