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AustraliaVIC
VCE 11 General 2023

11.05 Trigonometry of obtuse angles

Worksheet
Types of angles
1

Classify the following angles as one of the following:

  • Acute

  • Obtuse

  • Right-angled

  • Straight

  • Reflex

  • Revolution

a
b
c
d
e
f
g
h
i
j
k
l
m
n
o
Unit circle
2

Evaluate the following, correct to two decimal places:

a

\cos 126 \degree

b

\sin 146 \degree

3

Write the following trigonometric ratios using an acute angle:

a

\sin 147 \degree

b

\cos 165 \degree

c

\sin 125 \degree

d

\cos 160 \degree

e

\sin 91 \degree

f

\cos 120 \degree

4

In the following graphs, angle a is in standard position with its terminal side intersecting the circle at the given point P :

i

Find \sin a.

ii

Find \cos a.

a

P \left(\dfrac{7}{25}, \dfrac{24}{25}\right)

-1
1
x
-1
1
y
b

P \left( - \dfrac{24}{25} , \dfrac{7}{25}\right)

-1
1
x
-1
1
y
c

P\left( - 0.8824 , 0.4706\right)

-1
1
x
-1
1
y
Sine and cosine ratios of obtuse angles
5

Consider the unit semi-circle shown below:

a

Evaluate:

i

\sin 60 \degree

ii

\cos 60 \degree

b

State the coordinates of point B.

c

Hence, evaluate:

i

\sin 120 \degree

ii

\cos 120 \degree

6

Consider the unit semi-circle shown below:

a

Evaluate:

i

\sin 45 \degree

ii

\cos 45 \degree

b

State the coordinates of point B.

c

Hence, evaluate:

i

\sin 135 \degree

ii

\cos 135 \degree

7

The diagram shows P, which represents a rotation of 66 \degree around the unit circle:

a

Evaluate the following to two decimal places:

i

\sin 66 \degree

ii

\cos 66 \degree

b

State the coordinates of point P.

c

Hence, find the coordinates of the point on the unit circle that represents a rotation of 114 \degree.

d

Evaluate the following to two decimal places:

i

\sin 114 \degree

ii

\cos 114 \degree

iii

\tan 114 \degree

8

Find the solutions, to the nearest degree, for the following equations where 0 \degree \leq \theta \leq 180 \degree:

a

\sin \theta = 0.7071

b

\cos \theta = 0.67

c

\sin \theta = 0.65

d

\cos \theta = - 0.22

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Outcomes

U2.AoS4.3

the definition of sine and cosine for angles up to 180°

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