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iGCSE (2021 Edition)

20.10 Exact values (Extended)

Worksheet
Exact value triangles
1

Find the exact value of the following:

a

\sin 30 \degree

b

\sin 60 \degree

c

\sin 45 \degree

d

\cos 45 \degree

e

\cos 60 \degree

f

\cos 30 \degree

g

\tan 60 \degree

h

\tan 45 \degree

i

\tan 30 \degree

2

Evaluate the following expressions, leaving your answer in exact, rationalised form:

a
\dfrac{\sin 60 \degree}{\cos 30 \degree}
b
\sin 45 \degree \cos 30 \degree
c
\sin 45 \degree + \cos 30 \degree
d
\sin 45 \degree \cos 60 \degree + \tan 45 \degree
Unknown sides
3

Find the exact value of the pronumeral in the following triangles:

a
b
c
d
4

Consider the given triangle:

a

Find the exact length of side a.

b

Find the exact length of side b.

5

For each of the following triangles:

i

Find the exact value of x.

ii

Find the exact value of y.

a
b
6

Consider the unknown lengths in the given figure:

a

Find m.

b

Find t.

Unknown angles
7

\theta is an angle in a right-angled triangle. Find the value of \theta in the following equations:

a

\cos \theta = \dfrac{1}{2}

b

\sin \theta = \dfrac{\sqrt{3}}{2}

c

\sin \theta = \dfrac{1}{\sqrt{2}}

d

\tan \theta = \dfrac{1}{\sqrt{3}}

8

Find the value of \theta if \cos \theta = \dfrac{1}{\sqrt{2}} and \sin \theta = \dfrac{1}{\sqrt{2}}.

9

Given that \cos \theta = \dfrac{\sqrt{3}}{2} and \sin \theta = \dfrac{1}{2}:

a

Find the value of \theta.

b

Find the value of \tan \theta.

10

Find the unknown \theta in the following triangles:

a
b
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