[Complete this worksheet without using a calculator. Leave your answers in surd form if necessary.]
1. Complete the following table.
q / sin q / cos q / tan q30° / /
45°
60°
2. Find the value of each of the following.
(a)
(b)
(c)
(d)
3. Find q in each of the following.
(a)
(b)
(c)
4. Find the unknown in each of the following figures.
(a)
In DABC,
(b)
In DDEF,
(c)
In DPQR,
(d)
In DXYZ,
[Complete this worksheet without using a calculator.]
1. Simplify the following.
(a)
(b)
(c)
(d)
(e)
2. If, find the values of cosq and tanq.
[Analysis: Draw DABC, where ÐB=q, ÐC=90°, AC=and AB=. i.e..]
By Pythagoras’ theorem,
3. If, find the value of.
[Analysis: Draw DABC, where ÐB=q, ÐC=90°, =and=. i.e..]
4. If, find the value of.
[Complete this worksheet without using a calculator.]
1. Find q in each of the following.
(a)
\
(b)
\
(c)
\
2. Simplify.
3. Find the values of the following.
(a)
(b)
4. Prove that each of the following is an identity.
(a)
L.H.S.
\
(b)
\
(c)
\
[In this worksheet, unless otherwise stated, give your answers correct to 3 significant figures if necessary.]
1. Find the gradients corresponding to the following angles of inclination.
(a) 46°
Gradient =tan()
( )
(b) 60°
(c) 85°
(d) 5°
2. Find the angles of inclination corresponding to the following gradients. (Give your answers correct to the nearest degree.)
(a) 0.75
Let q be the corresponding angle of inclination.
( )
\ The corresponding angle of inclination is.
(b)
(c)
3. A car travels 5km along a road with the gradient of.
(a) Find the angle of inclination of the road.
(b) Find the vertical rise and the horizontal run of the car travelled.
Let xkm and ykm be the vertical rise and the horizontal run of the car travelled respectively.
()
\ The vertical rise and the horizontal run of the car travelled areand
respectively.
[In this worksheet, give your answers correct to 3 significant figures if necessary.]
1. Referring to the figure,
(a) find the angle of elevation of A from C.
The angle of elevation of A from C is.
(b) find the angle of depression of D from A.
()
()
\ The angle of depression of D from A is.
2. In the figure, Tommy is at point A looking at an aeroplane. It is given that the aeroplane is 2000m above the ground at that moment. If the angle of elevation of the aeroplane from Tommy is 22°, find the actual distance between Tommy and the aeroplane at that moment.
In DABC,
()
\ The actual distance between Tommy and the aeroplane at that moment is.
3. In the figure, a school is 20m high. Amy is at point A which is 30m away from the school. Find the angle of depression of point A from point C at the top of the school.
()
()
\ The angle of depression of point A from point C at the top of the school is.
1. Complete the following table.
Compass bearing / True bearingN8°E
N40°W
S42°W
S86°E
010°
123°
215°
357°
2. Find the true bearing of B from A and the compass bearing of A from B in each of the following.
(a)
\ The true bearing of B from A is.
()
\ The compass bearing of A from B is.
(b)
\ The true bearing of B from A is.
\ The compass bearing of A from B is.
(c)
[In this worksheet, give your answers correct to 3 significant figures.]
1. Tracy walks 500m due south and then 1000m due east. Find the compass bearing of her destination from her starting point.
()
\ The compass bearing of her destination from her starting point is.
2. Mark starts at A. He walks 250m at a bearing of 300° to B, and then walks at a bearing of 180° to C, which is due west of A. Find the distance between A and C.
In DABC,
()
\ The distance between A and C is.
3. Mandy starts at A. She walks 5km along the direction N58°E to B, and then walks 8km along the direction S32°E to C.
(a) Find the true bearing of C from A.
()
In DABC,
()
()
\ The true bearing of C from A is.
(b) Find the distance between A and C.
By Pythagoras’ theorem,
()
\ The distance between A and C is.
(c) If Mandy walks back to A directly from C, which direction should she walk along?
()
()
()
10.23