Chapter Test for Trig Ratios
Chapter
Chapter 5
Section
Chapter Test for Trig Ratios
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Solutions 14 Videos
  • i)For the point, sketch the angle in standard position to determine all six trigonometric ratios.
  • ii) Determine the value of the principal' angle and the related acute angle,

P(-3, 0)

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Q1a
  • i)For the point, sketch the angle in standard position to determine all six trigonometric ratios.
  • ii) Determine the value of the principal' angle and the related acute angle,

S(-8, -6)

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Q1b

Given angle \theta where 0^o \leq \theta \leq 360^o, determine all possible angles for \theta.

\sin \theta = -\frac{1}{2}

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Q2a

Given angle \theta where 0^o \leq \theta \leq 360^o, determine all possible angles for \theta.

\cos \theta = \frac{\sqrt{3}}{2}

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Q2b

Given angle \theta where 0^o \leq \theta \leq 360^o, determine all possible angles for \theta.

\cot \theta = -1

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Q2c

Given angle \theta where 0^o \leq \theta \leq 360^o, determine all possible angles for \theta.

\sec \theta = -2

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Q2d

Given \cos \theta = - \frac{5}{13}. where the terminal arm of angle \theta lies in quadrant 2, evaluate each trigonometric expression.

a) \displaystyle \sin \theta \cos \theta

b) \displaystyle \cot \theta \tan \theta

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Q3

Prove each identity.

\displaystyle 1 + \tan^2 \theta = \sec^2\theta

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Q4a

Prove each identity.

\displaystyle 1 +\cos^2\alpha = \csc^2 \alpha

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Q4b

Find w to the nearest tenth of a metre.

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Q6a

Find w to the nearest tenth of a metre.

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Q6b

Given each set of information. determine how many triangles can be drawn. Calculate, then label, all side lengths to the nearest tenth and all interior angles to the nearest degree, where appropriate.

a = 1.5 cm, b =2.8 cm, and \angle A = 41^o.

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Q7a

Given each set of information. determine how many triangles can be drawn. Calculate, then label, all side lengths to the nearest tenth and all interior angles to the nearest degree, where appropriate.

a = 2.1 cm, b = 6.1 cm, and \angle A = 20^o.

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Q7b

To estimate the amount of usable lumber in a tree, Chitra must first estimate the height of the tree. From points A and B on the ground, she determined that the angles of elevation for a certain tree were 41° and 52°. respectively. The angle formed at the base of the tree between points A and B is 90^o. and A and B are 30 m apart. If the tree is perpendicular to the ground. what is its height to the nearest metre?

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Q8