5.Evaluate the following without using a calculator. Select the closest answer from the list provided.
a)tan 45 ◦sin 60 ◦p^2
3p
3
1p
p^2
31
11
2
b)tan 30 ◦ sin 60 ◦0 12
p
3
2 1
2 p 3p
3
2
c)sin 30 ◦ tan 45 ◦ sin 30 ◦p
3
2 ^1
p^1
3 p
3
1 7
2
p
3
d)tan 30 ◦tan 30 ◦sin 45 ◦
p
3
12
p
p^3
2
p^2
3p
2
12
p
p^2
3
e)sin 45 ◦sin 30 ◦cos 45 ◦
p
p^2
3
p^1
2
p^4
3 22
p
p^2
3
f)tan 60 ◦ tan 60 ◦ sin 60 ◦ p^13 ^12 p^12 ^11 p
3
2
g)cos 45 ◦ sin 60 ◦ sin 45 ◦ ^12 p^12 2 p^73 p
3
2
p^1
3
6.Use special angles to show that:
a)
sin 60 °
cos 60 °=tan 60 ° b)sin^245 °+cos^245 °= 1 c) cos 30 °=√
1 sin^230 °7.Use the definitions of the trigonometric ratios to answer the following questions:
a)Explain whysin 1 for all values of.
b)Explain whycos has a maximum value of 1.
c)Is there a maximum value fortan?For more exercises, visit http://www.everythingmaths.co.za and click on ’Practise Maths’.
1a.2FPW 1b.2FPX 1c.2FPY 1d.2FPZ 1e.2FQ2 1f.2FQ3 1g.2FQ4 1h.2FQ5
2.2FQ6 3.2FQ7 4a.2FQ8 4b.2FQ9 4c.2FQB 5a.2FQC 5b.2FQD 5c.2FQF
5d.2FQG 5e.2FQH 5f.2FQJ 5g.2FQK 6a.2FQM 6b.2FQN 6c.2FQP 7a.2FQQ
7b.2FQR 7c.2FQShttp://www.everythingmaths.co.za m.everythingmaths.co.za5.7 Solving trigonometric equations EMA3T
In this section we will first look at finding unknown lengths in right-angled triangles and then we will look at
finding unknown angles in right-angled triangles. Finally we will look at how to solve more general trigono-
metric equations.
120 5.7. Solving trigonometric equations