Reference no: EM131096685
Task 1:
1. Convert the following into degrees and minutes:
- 3Π/8 rads
- 1.26Π rads
2. Convert the following into radians
- 152° 15'
- 17° 56' 22"
3. on the circle below calculate:
a. the length of the major and minor arc and
b. the area of the major and minor sector
When r = 2.5cm and θ = Π/4 radians
c. For the following triangle produce a table stating the values of the sine, cosine and tangent of angles α and θ.
d. Determine the value of x in each of the following right angled triangles
Task 2 :
On a graph plot the following waveforms over a complete cycle:
- Y = 2sin (θ + 30)
- Y = 4Cos 3θ
- Y = 3Tan (θ/2)
Graph paper is available from www.papersnake.com
Task 3 :
1. A crank mechanism of a petrol engine is shown below. The arm OA is 10.0cm long and rotates clockwise about point central point O. The connecting rod AB is 40.0cm long and end B can only move horizontally along length OB.
In its starting position determine the angle B giving your answer in degrees and minutes
2. The diagram below shows two forces acting on object O. Calculate the magnitude of the resultant force using trigonometric methods where F1 = 7N, F2 = 4N and θ = 30°
To calculate the Resultant Force (FR)
FR = F1 + F2
3. A gear system is being designed where a small 30mm diameter cog is to be fitted between a 70mm diameter driving gear and a 90mm driven gear as shown below. Determine the value of the angle θ between the centre lines.
Calculate the volumes and surface reas of the following solids:
Solid 1: A cone with a radius of 5cm a nd a height of 12cm
Solid 2: The following solid prism
Solid 3: The following wooden block where r = 8cm
Solid 4: the following engineered block
Reasoned calculation (showing full working out) for each of the questions. Your answers should be given to 2 d.p.s with the correct units stated.
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