Trigonometry

Sine and cosine cannot be greater than 1 because they are the Y and X values of a point on the unit circle. Tangent, on the other hand, is sine over cosine, so its domain is (-infinity,+infinity), with an asymptote occurring every odd pi/2.

It is 28.3 grams, approx.

This is so much work that it is not worthwhile to do in practice, although the formulae themselves are actually quite simple. The basic method is to use a so-called "infinite series". The angle must be expressed in radians. If the angle is in degrees, multiply it by (pi/180), to get the equivalent angle in radians. Then, use the formula:

sin(x) = x - x3/3! + x5/5! - x7/7! + x9/9!...

The individual terms become smaller and smaller, quite quickly, so the idea is to continue adding more terms until you see that the terms become so small that you can ignore them (depending on the desired degree of accuracy). An expression like 5!, read "five factorial" or "the factorial of five", means to multiply all natural numbers up to five: 5! = 1 x 2 x 3 x 4 x 5.

Similarly,

cos(x) = 1 - x2/2! + x4/4! - x6/6! + x8/8!...

There is a more complicated formula for tan(x), or simply calculate as follows:

tan(x) = sin(x) / cos(x)

The formulae for sin(x) and cos(x) are derived from the Taylor expansion, explained in basic calculus books.

The answer to the question is given in the question!If you want to find the value of an algebraic expression, then you need to substitute numerical values for each of the variables in the expression, and then calculate and simplify the result.

23 : 100

0.766

Hypotenuse = 20/sin580 = 23.58356807

Length of ladder: rounded to 23.584 feet

There is no easy simplification.

A sphere is not usually divided into 4 quadrants. Dividing by 2 along each of the 3 orthogonal axes partitions the sphere into 8.

If you are standing 45m from the base of the tree and an imaginary lines from the tip of the tree to the ground forms a 26° angle with the ground, then the tree is 21.95 m tall.

(45m) * tan(26°) = 21.95 m

The exact value is 0.5*sqrt(3)

The problem x = 2 sin x cannot be solved by using algebraic methods.

One solution is to draw the graphs of y = x and y = 2 sin x.

The two lines will intersect. The values of x where the intersection takes place are the solutions to this problem.

You can tell from the graph that one solution is x=0 and verify this contention by noting that 2 sin(0) = 0.

You can find the other solution through numerical methods and there are many that will give you the correct solution. Perhaps the simplest is to start with a value of X like pi/2 and then take the average of 2*sin(X) and X. Using that as your new value, again take the average of 2*sin(X) and X. As you continue to do this, the value will get closer and closer to the desired value. After 20 steps or so, the precision of your calculator will probably be reached and you will have a pretty good answer of about 1.89549426703398. (A spreadsheet can be used to make these calculations pretty easily.)

the referance angle of 960 is -60degrees

u have to circle the graph twice so it would be 960-360-360=240 (the 360s are how many turns it takes because it only goes up to 360 degrees so you have to subtract 360 from 960 twice to get it a number that's not over 360). so u get 240 which is graph III the lower left corner and subtract it 180-240=-60.

the angle should be connected with the x-axis never the y-axis..so never subtract from 90 or 270.

90 to 180.

The inexact value of tan 330 is -0.577350, to six significant places.

The exact value cannot be represented as a single number because it is a non terminating decimal. To represent it exactly, consider that tan x is sin x over cos x, and that sin 330 is -0.5 and cos 330 is square root of 0.75. As a result, the exact value of tan 330 is -0.5 divided by square root of 0.75.

The sin of 30 is sqr(3)/2

so 6 * sqr(30) is 6 * sqr(3)/2

this is also 6/2 * sqr(3) which simplifies to 3 * sqr(3) which is approximately 5.19615242

ARJUN 57

There are several cases when you would want to use the law of sines. When you have angle angle side, angle side angle, or angle side side you would use the law of sines.

The cosine of 60 degrees is 0.5

The only rectilinear figure is a triangle, or one composed of several triangles joined together.

A guy wire attached to a tower 181 feet from the base (190 - 9) and making an angle of 21 degrees with respect to the ground is 505 feet long.

sin (21) = 181 / x

x = 181 / sin (21)

Note: An angle of 21 degrees with respect to the ground is unrealistic. It is probably more correct to say 21 degrees with respect to the tower, which is 69 degrees with respect to the ground. In this case, the guy wire is 194 feet long.

cos(73°) = sin(17°) = ~0.29237

The solution is found by applying the definition of complementary trig functions:

Cos (&Theta) = sin (90°-&Theta)

cos (62°) = sin (90°-62°)

Therefore the solution is sin 28°.

29.36 degrees. tan-1(45/80) = 29.36

It is 45 + 360*k deg or 135 + 360*k degrees where k is an integer.