© 2008  Rasmus ehf and Jóhann Ísak Pétursson

Test 3 Trig Rules 

Instructions.

Read each question carefully and choose the answer that you think is most likely to be correct. You can only choose one answer for each question. When you are ready, mark your answers in the spaces on the computer screen and click on the button 'Send answers'. Good luck

Do the following examples putting a check mark by the correct answer:

1.     Find the amplitude of the function f(x) = sin x + cos x?

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Possible answers:
A 1
B
C 2
D
1 +

2.    The wave f(x) = sin x − cos x is translated from the basic sine function. What translation is this?

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Possible answers:
A 45° to the left
B 60° to the left
C 45° to the right
D
60° to the right

3.   Find the distance of the top of the wave f(x) = 6 sin x + 8 cos x + 1 from the x axis

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Possible answers:
A 11
B 13
C 15
D 17

4.      Which of the following applies to the function
f(x) = 2 sin x + 3 cos x = 5?

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Possible answers:
A 50.8° translation to the right,
amplitude = Ö5
B 50.8° translation to the left
and amplitude = Ö5
C 50.8° translation to the right
and amplitude = 5
D 50.8° translation to the left
and amplitude = 5
 
5. Which of the functions below applies to this graph?
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Possible answers:
A f(x) = sin x + cos x
B f(x) = sin x − cos x
C f(x) = sin x + cos x
D f(x) = sin x − cos x
   
6.

Solve the equation 3 sin x − 4 cos x = 0 on the interval 0° x° < 360°.
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Possible answers:
A 0°
B 53.1°
C 53.1° og 233.1°
D 0°, 53.1°, 180° og 233.1°
 
7.

Solve the equation 3 sin x − 4 cos x = 4 on the interval 0° x° < 360°.
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Possible answers:
A 180°
B 0°og 180°
C 90° og 106.3°
D 106.3° og 180°

8.      Find all solutions of the equation 3 sin x − 4 cos x = 5.     

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Possible answers:
A 34.9° + k∙360°
B 143.1° + k∙360°
C 34.9° + k∙360° og 143.1° + k∙360°
D
−34.9° + n∙180°

9.     Find all solutions of the equation 3 sin x + 3 cos x = 3 in radians.

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Possible answers:
A p/6 + k∙2p
B p/6 + k∙p
C p/6 + k∙p og p/2 + k∙p
D p/6 + k∙2p og p/2 + k∙2p

10.     Find all solutions of the equation in degrees:

        2 sin x cos x  + 2 cos 2 x − 2 sin 2 x = 5

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Possible answers:
A 13.3° + k∙180°
B 26.6° + k∙360°
C 15° + k∙360° og 165° + k∙360°
D 15° + k∙360°, 45° + k∙180° og 165° + k∙360°

 

Percentage answered correctly =

Correct answers: Your answers: