Trigonometry

COS 16.5 = 0.7

To get this answer, type in tan(28) in your calculator. It should come out to be about .532. Make sure your calculator is in Degree mode.

As θ increases from 0 to π/2 (90o) sin θ increases until it reaches a maximum value of 1 when θ = π/2.

As θ increases from π/2 (90o) to 3π/2 (270o) sin θ decreases until it reaches a minimum value of -1 when θ = 3π/2.

As θ increases from 3π/2 (270o) to 3π (360o) sin θ increases until it reaches the value of 0 it had when θ = 0.

From this point, as θ increases (by the same amounts) sin θ repeats this same cyclic behaviour.

28

The Law of Sines: a/sin A = b/sin B = c/sin C

24/sin 42˚ = c/sin (180˚ - 42˚ - 87˚) since there are 180˚ in a triangle.

24/sin 42˚ = c/sin 51˚

c = 24(sin 51˚)/sin 42˚ ≈ 28

cos 71

tan(60°) = sqrt(3)

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.

Let x = theta, since it's easier to type, and is essentially the same variable. Since tan^2(x)=tan(x), you know that tan(x) must either be 1 or zero for this statement to be true. So let tan(x)=0, and solve on your calculator by taking the inverse. Similarly for, tan(x)=1

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.

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.

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

It is 66 deg 15 min 0 sec.

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

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.

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.

The Formula is Base*Height, or 1/2 Height (altitude of the triangle) * Base (of the Triangle) * height (Height of the prism)

sin(21 deg) = 0.3584

it equals 4