Trigonometry

arctan(0.5)

in degrees = 26.6 degrees

=====================================( you could call it 0.5 radians )

Satellite dishes are paraboloid in shape - that is, a parabola (a quadratic curve) rotated around its axis.

The shape has the property that rays entering it are reflected to its focus of the paraboloid. If the receiver is placed at that point, the signal is picked up from the broadcasting satellite over a wide field of view.

1.570796327

Sin(30) = 1/2

Sin(45) = root(2)/2

Sin(60) = root(3)/2

Cos(30) = root(3)/2

Cos(45) = root(2)/2

Cos(60) = 1/2

Tan(30) = root(3)/3

Tan(45) = 1

Tan(60) = root(3)

Csc(30) = 2

Csc(45) = root(2)

Csc(60) = 2root(3)/3

Sec(30) = 2root(3)/3

Sec(45) = root(2)

Sec(60) = 2

Cot(30) = root(3)

Cot(45) = 1

Cot(60) = root(3)/3

Allied angles are found on the transversal line that cuts through parallel lines and the 2 angles add up to 180 degrees

Assuming you know the angle of ascension, and the base, you can calculate the height by recalling that tangent theta is height over base. Simple algebra from there: height is tangent theta times base.

tan(61°) = 1.80405 (rounded)

A polygon is a plane figure which comprises one area bounded by three or more straight line segments. A general plane figure can have curved boundaries or sides that cross each other.

In a trigonometric equation, you can work to find a solution set which satisfy the given equation, so that you can move terms from one side to another in order to achieve it (or as we say we operate the same things to both sides).

But in a trigonometric identity, you only can manipulate separately each side, until you can get or not the same thing to both sides, that is to conclude if the given identity is true or false.

Sin(x) cos(x) = 1/2 of sin(2x)

It is 66 deg 15 min 0 sec.

The equations for projectiles shouldn't just have theta, they should have sin(theta) or cos(theta).

As long as you have your calculator set in the right mode, either will work when you evaluate sin or cosine.

Example: Say you have a projectile launched at 30 degrees above horizontal. In order to find the y velocity, you will have to calculate sin(30) with you calculator in degree mode. If instead you called this angle pi/6 (the same angle, just in radians), you could enter sin(pi/6) in your calculator in radians mode and get the same answer.

Sin (theta) can most easily be found on a scientific calculator. You can also approximate it with Taylor's Series...

sin(x) = SummationN=0toInfinity (-1N / (2N + 1) !) (x(2N+1)))

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

Using only the four terms above, you can approximate sin(x) within about 0.000003 in the interval x = [-1, +1].

Yes, because all sound waves can be modelled as sine (or cosine) waves, or combinations of sine waves.

If sin (theta) is 3/5, then sin2 (theta) is (3/5)2, or 9/25.

cos2(theta) = 1

cos2(theta) + sin2(theta) = 1 so sin2(theta) = 0

cos(2*theta) = cos2(theta) - sin2(theta) = 1 - 0 = 1

There are an enormous number of uses of trigonometry and trigonometric functions. For instance, the technique of triangulation is used in astronomy to measure the distance to nearby stars, in geography to measure distances between landmarks, and in satellite navigation systems. The sine and cosine functions are fundamental to the theory of periodic functions such as those that describe sound and light waves.

Fields that use trigonometry or trigonometric functions include astronomy (especially for locating apparent positions of celestial objects, in which spherical trigonometry is essential) and hence navigation (on the oceans, in aircraft, and in space), music theory, acoustics, optics, analysis of financial markets,electronics, probability theory, statistics, biology, medical imaging (CAT scans and ultrasound), pharmacy, chemistry, number theory (and hence cryptology),seismology, meteorology, oceanography, many physical sciences, land surveying and geodesy, architecture, phonetics, economics, electrical engineering,mechanical engineering, civil engineering, computer graphics, cartography, crystallography and game development.

sin(1,305) = sin(225) = -0.70711 (rounded) = 1/2 of the negative square root of 2.

arcsin(0.943)

= 1.23 ( in radian )

= 70.56 ( in degrees )

There are an enormous number of uses of trigonometry and trigonometric functions. For instance, the technique of triangulation is used in astronomy to measure the distance to nearby stars, in geography to measure distances between landmarks, and in satellite navigation systems. The sine and cosine functions are fundamental to the theory of periodic functions such as those that describe sound and light waves.

Fields that use trigonometry or trigonometric functions include astronomy (especially for locating apparent positions of celestial objects, in which spherical trigonometry is essential) and hence navigation (on the oceans, in aircraft, and in space), music theory, acoustics, optics, analysis of financial markets,electronics, probability theory, statistics, biology, medical imaging (CAT scans and ultrasound), pharmacy, chemistry, number theory (and hence cryptology),seismology, meteorology, oceanography, many physical sciences, land surveying and geodesy, architecture, phonetics, economics, electrical engineering,mechanical engineering, civil engineering, computer graphics, cartography, crystallography and game development.

6

Precalculus is supposed to be a stringent and comprehensive review of both algebra and trigonometry. This is in preparation for calculus which uses both algebra and trig extensively.

Use the trigonometric relations and identities.

COS squared Theta + SIN squared Theta = 1; where Theta is the angles measurement in degrees.