Multiple Choice
Identify the
choice that best completes the statement or answers the question.
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1.
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What are the three other angles in standard position that have a reference angle
of 40°?
A | 85°, 130°, 220° | C | 130°, 220°, 310° | B | 80°, 120°, 160° | D | 140°, 220°, 320° |
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2.
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What is the exact sine of ÐB? 
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3.
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The coordinates of a point P on the terminal arm of an angle are shown. What are
the exact trigonometric ratios for  ,  , and  ? 
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4.
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Marco is 500 m due east of the centre of the park. His friend Ray is 500 m due
south of the centre of the park. Which is the correct expression for the exact distance between the
two boys?
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5.
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Determine the length of x, to the nearest tenth of a centimetre. 
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6.
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Which strategy would be best to solve for x in the triangle
shown?  A | primary trigonometric ratios | C | sine law | B | cosine
law | D | none of the
above |
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7.
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Which strategy would be best to use to solve for x?  A | cosine law | C | sine law | B | primary trigonometric ratios | D | none of the
above |
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8.
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Determine the measure of x, to the nearest tenth of a degree. 
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9.
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If  °, r = 11 cm, and
p = 12 cm, what is the length of q, to the nearest centimetre? 
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10.
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Solve the following triangle, rounding side lengths to the nearest tenth of a
unit and angle measures to the nearest degree.  Diagram not drawn to scale.
 , b =
17, a = 23.5
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Short Answer
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1.
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The hypotenuse of a right isosceles triangle is 5 cm long.
a) Write
an exact expression for the base and the height of the right triangle, using primary trigonometric
ratios.
b) Use your expressions to determine the exact area of the triangle.
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2.
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In acute  , o = 7 cm, p = 9 cm, and  . Solve  .
What type of triangle is this?
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3.
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a) For the given trigonometric ratio, determine two other angles that
give the same value.
i) sin 45°
ii) tan 300°
iii) cos
120°
b) Explain how you determined the angles in part a).
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Problem
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1.
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a) Without using a calculator, determine two angles between 0° and
360° that have a sine ratio of  . b) Use a calculator and a diagram to verify your
answers to part a).
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2.
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Two sides of a triangle are x units and y units in length. The
angle between them is q. Prove that the area of the triangle is
 .
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