Section Seven Trigonometry

Question 1

What is trigonometry?

Answer 1

The branch of mathematics that deals with the relationships between the sides and angles of triangles.

Question 2

What is the longest side of a right triangle called?

Answer 2

The hypotenuse.

Question 3

What is the side opposite the angle called?

Answer 3

The opposite side.

Question 4

What is the side next to the angle called (other than the hypotenuse)?

Answer 4

The adjacent side.

Question 5

What are the three primary trigonometric functions?

Answer 5

Sine (sin), Cosine (cos), and Tangent (tan).

Question 6

What is the sine of an angle defined as?

Answer 6

sin(θ) = Opposite ÷ Hypotenuse.

Question 7

What is the cosine of an angle defined as?

Answer 7

cos(θ) = Adjacent ÷ Hypotenuse.

Question 8

What is the tangent of an angle defined as?

Answer 8

tan(θ) = Opposite ÷ Adjacent.

Question 9

How do you find the angle if you know the sides?

Answer 9

Use inverse functions: sin⁻¹, cos⁻¹, or tan⁻¹.

Question 10

What is the Pythagorean theorem?

Answer 10

a² + b² = c², where c is the hypotenuse.

Question 11

If the rise is 3 and the run is 4, what is the hypotenuse?

Answer 11

5 (because 3² + 4² = 5²).

Question 12

What is the tangent formula used for in pipe layout?

Answer 12

To find the angle of an offset when rise and run are known: tan(θ) = rise ÷ run.

Question 13

How do you find the rise if you know the run and angle?

Answer 13

rise = run × tan(θ).

Question 14

How do you find the run if you know the rise and angle?

Answer 14

run = rise ÷ tan(θ).

Question 15

How do you find the hypotenuse (travel) if you know rise and run?

Answer 15

travel = √(rise² + run²).

Question 16

How do you find the adjacent side if you know the hypotenuse and angle?

Answer 16

adjacent = hypotenuse × cos(θ).

Question 17

How do you find the opposite side if you know the hypotenuse and angle?

Answer 17

opposite = hypotenuse × sin(θ).

Question 18

What are the reciprocal trigonometric functions?

Answer 18

Cosecant (csc = 1/sin), Secant (sec = 1/cos), and Cotangent (cot = 1/tan).

Question 19

What is an angle measured in?

Answer 19

Degrees (°) or radians.

Question 20

How many degrees are in a right angle?

Answer 20

90°.

Question 21

How many degrees are in a complete circle?

Answer 21

360°.

Question 22

What is the relationship between degrees and radians?

Answer 22

180° = π radians.

Question 23

What are the trigonometric ratios for a 30°–60°–90° triangle?

Answer 23

Opposite (30°) = ½ hypotenuse

Question 24

What are the trigonometric ratios for a 45°–45°–90° triangle?

Answer 24

Opposite = Adjacent = 0.707 × hypotenuse.

Question 25

How can trigonometry be applied in pipefitting?

Answer 25

Used to calculate travel, run, rise, and angles for offsets and rolling offsets.

Question 26

What is the sine law (Law of Sines)?

Answer 26

a/sin(A) = b/sin(B) = c/sin(C).

Question 27

What is the cosine law (Law of Cosines)?

Answer 27

c² = a² + b² − 2ab × cos(C).

Question 28

When is the Law of Cosines used?

Answer 28

When you know two sides and the included angle or all three sides.

Question 29

When is the Law of Sines used?

Answer 29

When you know one side and two angles or two sides and a non-included angle.

Question 30

What is the tangent of 45°?

Answer 30

1 (because opposite = adjacent).

Question 31

What is the sine of 30°?

Answer 31

0.5.

Question 32

What is the cosine of 60°?

Answer 32

0.5.

Question 33

What is the sine of 45°?

Answer 33

0.707.

Question 34

What is the cosine of 45°?

Answer 34

0.707.

Question 35

What is the tangent of 30°?

Answer 35

0.577.

Question 36

What is the tangent of 60°?

Answer 36

1.732.

Question 37

What is the cosine of 0°?

Answer 37

1

Question 38

What is the sine of 0°?

Answer 38

0

Question 39

What does the term “angle of elevation” mean?

Answer 39

The angle measured upward from a horizontal reference line.

Question 40

What does the term “angle of depression” mean?

Answer 40

The angle measured downward from a horizontal reference line.

Question 41

What is a trigonometric table used for?

Answer 41

To find sines, cosines, and tangents for specific angles.

Question 42

How can a scientific calculator be used in trigonometry?

Answer 42

By entering the angle and selecting sin, cos, or tan to find ratios or using inverse keys to find angles.