S3 Trigonometry and Applications Flashcards
(tan a) x (cos a)
sin a
sin2a + cos2a
1
sin (90º-a)
cos a
cos (90º-a)
sin a
tan (90º-a)
1/tan a
if sin a = cos b, then…
a + b = 90º
{(tan a)/(sin (90º-a))} x sin a
1
(sin a + cos a)2 + (sin a - cos a)2
2
What is inclination?
The angle between the horizontal and the inclined plane. The larger the inclination, the steeper the plane.
What is gradient?
vertical distance/horizontal distance
Given the inclination of a line a, its gradient is…
tan a
Given the gradient of a line y/x, its inclination is…
tan-1(y/x)
Consider the gradient in form 1:n. The plane is steeper if…
n is smaller
Consider the gradient in form tan a. The plane is steeper if…
a is larger/tan a is larger.
How do we obtain the actual distance from a map with scale 1:k?
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.
Features of angles of elevation and depression
One of the arms of the angles must be a horizontal line.
What is true bearing?
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.
What is compass bearing?
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.
