Trigonometry

1/2(x-ln(sin(x)+cos(x)))

It comes from the Latin phrase "medium aevum," meaning literally "the Middle Age."

The distance formula using Pythagorean theorem: trig values trig formulas triangle abc trigonometric concepts trigonometric formulas.

It would have been much simpler if this browser had halfway decent graphic facilities but it does not so you may have do a few sketches as you go along..

The bowl is tipped by 35 deg so the diameter of the bowl makes a 35 deg angle with the horizontal. The surface of the water must be horizontal and so that makes an angle of 35 deg with the tipped diameter.

Therefore [in cross section] the water occupies a segment of a circle such that the angles between the water surface and the radii at both ends on the segment are 35 deg. Therefore the segment subtends an angle of 110 deg at the centre. Also, the radii are 20 cm.

In the triangle formed by the water surface and the sides of the segment, the distance from the centre of the bowl to the water surface is 20*sin(35) = 11.47 cm. Therefore, the depth of the water is 20 - 11.47 = 8.53 cm.

4

For solving the properties of triangles

It is [(2a+2h+5) - (2a+5)]/h = 2h/h = 2

It can be but need not be.

-sqrt2

3 ≤ M ≤ 4 or M belongs to the set [3,4] - using the square parentheses.

The 'included' angle between sides 9 and 8.5 is 106.225 and so the area of the triangle is 0.5*9*8.5*sine(106.225) = 36.727 square cm rounded up to 3 decimal places.

cos90=0

They typically aren't useful in your everyday life unless your job requires them.

There r 3 formulas for cube.

Volume- (side X side X side)

Curved surface area- 4(side X side)

Total surface area- 6(side X side)

Radians.

tan(54)

= 0.6738

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Yes. (Theta in radians, and then approximately, not exactly.)

when trying to find the angle of a right triangle using only the opposite leg and the hypotenuse, eg. angle =sin opp leg over hyp

* * * * *

Also to find the area of a triangle if two sides and the included angle are known.

Or the area of a sector of a circle.

Yes.

If you have a quadratic function with real coefficients then it can have:

two distinct real roots, or

a real double root (two coincidental roots), or

no real roots.

In the last case, it has two complex roots which are conjugates of one another.

tan3theta

Double verticle lines surrounding an expression means to take the absolute value of the expression.

The absolute value of an expression is the expression if it is positive, and the negative of the expression if it is negative, i.e. the unsigned distance from zero. Analytically, in order to process the expression, the absolute value of an expression is also the square root of the square of the expression.

cos-1(0.74) = 42.26858443 degrees

Take the number you have out of the whole, then dived it by the whole number. Multiply the resulting number by 100 and that's your percent.

Example:

What percentage is 7 of 10?

7 / 10= .7

.7 x 100 = 70

7 is 70% of 10.