S3 Trigonometry and Applications

Question 1

(tan a) x (cos a)

Answer 1

sin a

Question 2

sin²a + cos²a

Answer 2

1

Question 3

sin (90º-a)

Answer 3

cos a

Question 4

cos (90º-a)

Answer 4

sin a

Question 5

tan (90º-a)

Answer 5

1/tan a

Question 6

if sin a = cos b, then…

Answer 6

a + b = 90º

Question 7

{(tan a)/(sin (90º-a))} x sin a

Answer 7

1

Question 8

(sin a + cos a)² + (sin a - cos a)²

Answer 8

2

Question 9

What is inclination?

Answer 9

The angle between the horizontal and the inclined plane. The larger the inclination, the steeper the plane.

Question 10

What is gradient?

Answer 10

vertical distance/horizontal distance

Question 11

Given the inclination of a line a, its gradient is…

Answer 11

tan a

Question 12

Given the gradient of a line y/x, its inclination is…

Answer 12

tan^-1(y/x)

Question 13

Consider the gradient in form 1:n. The plane is steeper if…

Answer 13

n is smaller

Question 14

Consider the gradient in form tan a. The plane is steeper if…

Answer 14

a is larger/tan a is larger.

Question 15

How do we obtain the actual distance from a map with scale 1:k?

Answer 15

Find the distance on the map. Multiply it by k as the horizontal distance. Then, through reading counter lines, find the vertical distance. Find the actual distance by Pythagoras’ theorem.

Question 16

Features of angles of elevation and depression

Answer 16

One of the arms of the angles must be a horizontal line.

Question 17

What is true bearing?

Answer 17

True bearing describes the relative position of two objects on the same plane. It is an angle measure starting from the north and in a clockwise direction. The integral part of true bearing must be written in 3 digits.

Question 18

What is compass bearing?

Answer 18

Compass bearing, or reduced bearing, is in the format N/S (angle) E/W. The angle is first measured from the north or south depending on which value is smaller, and then measured towards the east or west similarly. The angel in between two letters is between 0 and 90 degrees.