Mid Chapter Review on Trig
Chapter
Chapter 5
Section
Mid Chapter Review on Trig
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Solutions 22 Videos

Evaluate to four decimal places.

\csc 20^o

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Q1a

Evaluate to four decimal places.

\cot 10^o

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Q1b

Evaluate to four decimal places.

\sec 75^o

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Q1c

Evaluate to four decimal places.

\csc 81^o

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Q1d

Determine the value of \theta to the nearest degree if 0^o\leq \theta \leq 90^o.

\displaystyle \cot \theta = 0.8701

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Q2a

Determine the value of \theta to the nearest degree if 0^o\leq \theta \leq 90^o.

\displaystyle \sec \theta = 4.1011

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Q2b

Determine the value of \theta to the nearest degree if 0^o\leq \theta \leq 90^o.

\displaystyle \csc \theta = 1.6406

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Q2c

Determine the value of \theta to the nearest degree if 0^o\leq \theta \leq 90^o.

\displaystyle \sec \theta = 2.4312

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Q2d

A trigonometric ratio is \frac{7}{5}. What ratio could it be, and what angle might it be referring to?

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Q3

Clark is attaching a rope to the top of the mast of her sailboat so that she can lower the sail to the ground to do some repairs. The mast is 8.3 m long, and with her eyes level with the base of the mast, the top form an angle 31^o with the ground. How much rope does Claire need if 0.5 m of rope is required tot tie to the mast? Round your answer to the nearest tenth of a metre.

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Q4

If \csc \theta < \sec \theta and \theta is acute, what do you know about \theta?

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Q5

Determine the exact value of each trigonometric ratio.

\displaystyle \begin{array}{ccccc} &(a) \phantom{.} \sin 60^o &(a) \phantom{.} \csc 30^o \\ &(c) \phantom{.} \tan 45^o &(d) \phantom{.} \sec 45^o \end{array}

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Q6

Given \triangle ABC as shown,

a) determine the exact measure of each unknown side if \sin \alpha = \frac{1}{2}.

b) determine the exact values of the primary trigonometric ratios for \angle A and \angle DBC.

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Q7

i) Sketch each angle in standard position. Use the sketch to determine the exact value of the given trigonometric ratio.

ii) If 0^o \leq \theta \leq 360^o, state all values of \theta that have the same given trigonometric ratio.

\sin 120^o

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Q8a

i) Sketch each angle in standard position. Use the sketch to determine the exact value of the given trigonometric ratio.

ii) If 0^o \leq \theta \leq 360^o, state all values of \theta that have the same given trigonometric ratio.

\cos 225^o

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Q8b

i) Sketch each angle in standard position. Use the sketch to determine the exact value of the given trigonometric ratio.

ii) If 0^o \leq \theta \leq 360^o, state all values of \theta that have the same given trigonometric ratio.

\tan 330^o

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Q8c

i) Sketch each angle in standard position. Use the sketch to determine the exact value of the given trigonometric ratio.

ii) If 0^o \leq \theta \leq 360^o, state all values of \theta that have the same given trigonometric ratio.

\cos 300^o

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Q8d

P(-9, 4) lies on the terminal arm of an angle in standard position.

a) Sketch the principal angle \theta.

b) What is the value of the related acute angle \beta to the nearest degree?

c) What is the value of the principal angle \theta to the nearest degree?

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Q9

Is it possible that \cos \theta = \frac{4}{5} has 3 different answer when 0^o \leq \theta \leq 360^o? Explain. If not, how many answer can it have?

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Q10

Given \tan \theta = -\frac{15}{8}, where 90^o \leq \theta \leq 180^o,

a) state the other five trigonometric ratios as fractions.

b) determine the value of \theta to the nearest degree.

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Q11

If \sin \theta = -0.8190 and 0^o \leq \theta \leq 360^o, determine the value of \theta to the nearest degree.

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Q12

\theta lies in quadrant II. Without using a calculator, which ratios must be false? Justify your reasoning.

a) \cos \theta = 2.3151

b) \tan \theta = 2.3151

c) \sec \theta = 2.3151

d) \csc \theta = 2.3151

e) \cot \theta = 2.3151

f) \sin \theta = 2.3151

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Q13