CIS034-1 Practical A1 PDF

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CIS034-1 Engineering Mathematics Practical Exercise A1 The object this week is to get some practice at using the properties of triangles. There will also be a short diagnostic test, which does not count towards your grade, but which just lets us know about your prior mathematical knowledge. 1.

Express each ratio as sine, cosine, etc of angle α, β, γ or δ. DE =¿ DF

GI =¿ GH

E

H α

I

KL =¿ JK K

F

D

β

γ

MN =¿ NO O

L M δ

J G 2.

3.

N

Evaluate the following to 2 decimal places. You can use a calculator, for example the Windows 10 Calculator app in “Scientific” mode. a.

sin 35 °

b.

cos 47°

c.

tan 21 °

Find the exact values of the following. You can use the “standard triangles” values on the formula sheet. a.

cos ( 45° ) sin (45 °)

b.

( 60 ° )+¿ tan (30 °) tan ¿

c.

( 60 ° )+ ¿ tan (60°) sin ¿

d.

sin ( 45° ) ( tan 45 ° ) cos ( 45 ° )

e.

cos ( 45° ) +sin (60 °)

f.

( 30 ° )+¿ cos ( 60 ° ) sin ( 30 ° ) sin ( 60 ° ) cos ¿

4.

Express 2.5 radians in degrees.

5.

If a right-angled triangle has a base of 6 m and a hypotenuse of 13.2 m, what is its height?

6.

A ladder of length 6 m is placed against a wall. The greatest angle it can make to the ground and still be stable is 70°. Find the maximum reach of the ladder vertically up the wall.

7.

A road has a gradient of 1 in 10 (that is it rises 1 m for every 10 m horizontally). If a car travels 30 m along the road, how far has it travelled in a horizontal direction and how far has it risen?

8.

A statue is such that at a certain time of day, when the sun makes an angle of approximately 63° with the ground, the length of the shadow is 10.2 m. Estimate the height of the statue.

9.

What is the total size of the angles of a triangle?

10.

What is the total size of the angles of a quadrilateral (a shape with 4 straight sides)?

11.

What is the total size of the angles of a pentagon (a shape with 5 straight sides)?

(Steps 2 to 8 are based on problems in exercise 4(a) and exercise 4.19 of Singh, Engineering Mathematics Through Applications, 2011 and example 6.7, exerecise 6.4 and exercise 6.5 of Attenborough, Mathematics for Electrical Engineering and Computing Background Mathematics Notes, 2003)

Exercise A1 revision 7 Windows 10...