Unit 15 Basic Trigonometry and Vectors

Question 1

define a right triangle.

Answer 1

1

Question 2

discuss the Pythagorean theorem.

Answer 2

1

Question 3

solve problems concerning right triangles using the Pythagorean theorem.

Answer 3

1

Question 4

solve problems using sines, cosines, and tangents.

Answer 4

1

Question 5

Preview Many AC formulas are based on right triangles,

Answer 5

depending on the type of load, the voltage and current in an AC circuit can be out of phase with each other by approximately 90° .

Question 6

Pythagorean theorem:

Answer 6

C² = a² + b²

Question 7

If the lengths of the two sides are known, the length of the hypotenuse can be found using the formula

Answer 7

C= √a²+b²

Question 8

Sines, Cosines, and Tangents . A second important concept concerning right triangles is the relationship of the length of the sides to the angles.

Answer 8

one angle is always 90° , only the two angles that are not right angles are of concern. Another important fact concerning triangles is that the sum of the angles of any triangle equals 180 ° ; because one angle of a right triangle is 90 °

Question 9

It was discovered long ago that the number of degrees in each of these two angles is proportional to the lengths of the three sides.

Answer 9

This relationship is expressed as the sine, cosine, or tangent of a particular angle. The function used is determined by which sides are known and which of the two angles is to be found.

Question 10

Vectors

Answer 10

A vector is a line that indicates both magnitude and direction.

Question 11

What are Vectors

Answer 11

A vector is a line that indicates both magnitude and direction. The magnitude is indicated by its length, and the direction is indicated by its angle of rotation from 0 8 .

Question 12

What is Scalars

Answer 12

Vectors should not be confused with scalars, which are used to represent magnitude only and do not take direction into consideration.

Question 13

vectors contain,

Answer 13

both magnitude and direction

Question 14

resultant

Answer 14

This means that 4 volts of the 6-volt battery A would have to be used to overcome the voltage of battery B. The resultant would be a vector with a magnitude of 2 volts in the same direction as the

Question 15

Using the right triangle is just one method of graphically showing how an-gular quantities can be added.

Another method Is

Answer 15

vectors.

Question 16

The magnitude is indicated by

and the direction is indicated by

Answer 16

its length,

its angle of rotation from 0° ,

or Direction.

Question 17

Scalars

Vectors should not be confused with scalars, which are used to represent

Answer 17

magnitude only and do not take direction into consideration.