Trigonometry

Question 1

What is the Opposite side (O)?

Answer 1

The side opposite the specified angle.

Question 2

What is the Adjacent side (A)?

Answer 2

The side next to the specified angle.

Question 3

What is sin(𝜃)?

Answer 3

O/H

Question 4

What is cos(𝜃)?

Answer 4

A/H

Question 5

What is tan(𝜃)?

Answer 5

O/A

Question 6

What is sin(0°), sin(30°), sin(60°), sin(45°), sin(90°)?

Answer 6

0, 1/2, [rt2(3)]/2, [rt2(2)]/2, 1

Question 7

What is cos(0°), cos(30°), cos(60°), cos(45°), cos(90°)?

Answer 7

1, [rt2(3)]/2, 1/2, [rt2(2)]/2, 0

Question 8

What is tan(0°), tan(30°), tan(60°), tan(45°), tan(90°)?

Answer 8

0, [rt2(3)]/3, rt2(3), 1, Undefined

Question 9

What is O?

Answer 9

Hsin(𝜃) or Atan(𝜃)

Question 10

What is A?

Answer 10

Hcos(𝜃) or O/tan(𝜃)

Question 11

What is H?

Answer 11

O/sin(𝜃) or A/cos(𝜃)

Question 12

What are (sin^-1)(O/H), (cos^-1)(A/H) and (tan^-1)(O/A)?

Answer 12

Functions to the -1 are the inverse of the original function so all of these statements equal 𝜃.

Question 13

What is the unit circle?

Answer 13

A circle with a radius of one that is put around the origin. The angle can then move around the circle and at any given angle, the x coordinate is cos(𝜃) and the y coordinate is sin(𝜃).

Question 14

What forms do the graphs sin(x), cos(x) and tan(x) take?

Answer 14

sin(x) and cos(x) take the form of a wave with a maximum of 1 and a minimum of -1. The former hits the origin while the latter hits (0, 1). tan(x) takes the form of separate curved lines stretching to infinity.

Question 15

If A is the angle opposite side a and B is the angle opposite side b etc. what is the sine rule?

Answer 15

a/sin(A) = b/sin(B) = c/sin(C) for any triangle. You can use it to work out a side when two angles and an opposite side are known and an angle when two sides and an opposite angle are known.

Question 16

If A is the angle opposite side a, what is the cosine rule?

Answer 16

a^2 = b^2 + c^2 - 2bc cos(A) or cos(A) = (b^2 + c^2 - a^2)/2bc for any triangle. You can use it to work out a side when two sides and the angle in between them are known and an angle when three sides are known.

Question 17

What can be used to find the area of a triangle?

Answer 17

If /c is the angle between a and b then the area is [ab sin(C)]/2.