How do you go from sin to CSC?

The secant of x is 1 divided by the cosine of x: sec x = 1 cos x , and the cosecant of x is defined to be 1 divided by the sine of x: csc x = 1 sin x .

What is the importance of algebraic expression?

Algebraic expressions play an important role in the mathematics curriculum and in mathematics in general. In order to progress and do well in mathematics, students need to be able to read and write expressions, and to be skilled in computations and manipulations of algebraic expressions.

Which country invented algebra?

Both of these civilizations used algebra in different ways and for different reasons, but it’s generally accepted that it was the Babylonians who first made basic use of algebra and pioneered its beginnings in the field of mathematics. There is evidence of this that dates back as far as 1900 to 1600 BC.

How trigonometry is used in real life?

Trigonometry can be used to roof a house, to make the roof inclined ( in the case of single individual bungalows) and the height of the roof in buildings etc. It is used naval and aviation industries. It is used in cartography (creation of maps). Also trigonometry has its applications in satellite systems.

How is sin calculated?

In a right triangle, the sine of an angle is the length of the opposite side divided by the length of the hypotenuse. In any right triangle, the sine of an angle x is the length of the opposite side (O) divided by the length of the hypotenuse (H).

Why do we use sine?

The sine function is defined as the ratio of the side of the triangle opposite the angle divided by the hypotenuse. This ratio can be used to solve problems involving distance or height, or if you need to know an angle measure. Example: To find the length of the side opposite the angle, d, we use the sine function.

What is sin equal to?

Always, always, the sine of an angle is equal to the opposite side divided by the hypotenuse (opp/hyp in the diagram). The cosine is equal to the adjacent side divided by the hypotenuse (adj/hyp). (1) Memorize: sine = (opposite side) / hypotenuse. cosine = (adjacent side) / hypotenuse.

Is Trig a calculus?

calculus involves the concepts of derivatives and integrals of functions. trig functions are one class of functions. so trig is more the study of one class of examples and calculus is an idea. in practice one applies the idea behind calculus to examples like those found in trig.

Why is algebra important in real life?

Algebra is an important life skill worth understanding well. It moves us beyond basic math and prepares us for statistics and calculus. Algebra is useful around the house and in analyzing information in the news. It also reinforces logical thinking and is beautiful.

How do you prove identity?

For instance, sin(x) = 1/csc(x) is an identity. To “prove” an identity, you have to use logical steps to show that one side of the equation can be transformed into the other side of the equation. You do not plug values into the identity to “prove” anything.

Why is it called trigonometry?

The word trigonometry comes from the Greek words trigonon (“triangle”) and metron (“to measure”).

How do doctors use trigonometry?

Trigonometry is used in orthopedics to find the deviation of a vertebra in degrees and know if the nerves are damaged. It is also used to mold prosthetic arms and legs that measurements are tailored to allow operation close to the original member.

What are the six trig functions?

There are six trigonometric ratios, sine, cosine, tangent, cosecant, secant and cotangent. These six trigonometric ratios are abbreviated as sin, cos, tan, csc, sec, cot.

Is algebra really necessary?

Algebra is a prerequisite for virtually all college-level mathematics courses, such as precalculus, calculus, linear algebra, statistics and probability, and more advanced mathematics courses. An understanding of algebra is also assumed in geometry and trigonometry courses.

What job uses trigonometry?

Trigonometry is used by engineers, medical services technicians, mathematicians, data entry specialists, loggers, statisticians, actuaries, drafters, chemists, economists, physicists, registered nurses, building inspectors, boilermakers, machinists and millwrights.

How is math used in real life?

1. Math Helps You Build Things. Figuring the total amount of concrete needed for a slab; accurately measuring lengths, widths, and angles; and estimating project costs are just a few of the many cases in which math is necessary for real-life home improvement projects.

What is cos 2x identity?

cos(2x) = cos^2(x) – sin^2(x) = 2 cos^2(x) – 1 = 1 – 2 sin^2(x) tan(2x) = 2 tan(x) / (1 – tan^2(x)) sin^2(x) = 1/2 – 1/2 cos(2x) cos^2(x) = 1/2 + 1/2 cos(2x) sin x – sin y = 2 sin( (x – y)/2 ) cos( (x + y)/2 )

What sine means?

1 : the trigonometric function that for an acute angle is the ratio between the leg opposite the angle when it is considered part of a right triangle and the hypotenuse.