PreCalculus Honors

Unit Test #5

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Part 1: Calculator Allowed

 

1.

Give two angles that are coterminal with 11π 18 .

(3)

11π 18 2π= 11π 18 36π 18 = 25π 18 , or 11π 18 +2π= 11π 18 + 36π 18 = 47π 18

 

2.

Evaluate: cos 10

(2)

cos 10 0.8391 (remember that you should be in radians)

 

3.

Evaluate: sin 1 2 3

(2)

sin 1 2 3 0.7297 (this should be in radians as well)

 

4.

The angle of inclination of a mountain with triple black diamond ski trails is 65°. If a skier at the top of the mountain is at an elevation of 4000 feet, how long is the ski run from the top to the base of the mountain?

(5)

Perhaps a picture?

An Image

 

An equation to solve this would be sin65°= 4000 x x= 4000 sin65° 4413.5117.

The ski run is 4413.5117 feet long.

 

5.

What is the angle of inclination required to observe a drone flying at an altitude of 40 feet when its distance from the observer is 250 feet?

(5)

Another picture?

An Image

 

The equation: sinθ= 40 250 θ= sin 1 40 250 9.2069°

 

PreCalculus Honors

Unit Test #5

 

Part 2: No Calculator Allowed

 

An Image

6.

Find the value of the trigonometric function indicated above.

(4)

First, the third side: 5 2 + 12 2 = h 2 25+144= h 2 169= h 2 13=h. Since secant is hypotenuse over adjacent, secθ= 13 12 .

 

7.

Convert to degrees: 7π 15

(4)

d 180° = 7π 15 π d 180° = 7 15 d= 7180 15 °= 712 °=84°

 

8.

Convert to radians: 105°

(4)

105° 180° = r π r= 105π 180 = 7π 12

 

9.

Evaluate: sin 7π 6

(2)

1 2

 

10.

Evaluate: cos 5π 4

(2)

1 2

 

11.

Evaluate: tan 4π 3

(2)

3

 

12.

Find cscθ, given that the terminal side of θ passes through the point 3,5 .

(4)

First off, the distance to the point: 3 2 + 5 2 = r 2 9+25= r 2 34= r 2 r= 34 . Since cscθ= y r , cscθ= 34 5 .

 

13.

Find the values of all other trigonometric functions if tanθ= 5 12 and cosθ<0.

(6)

Since cosθ<0 and tanθ<0 makes sinθ>0 (Quadrant 2). 12 2 + 5 2 = r 2 144+25= r 2 169= r 2 13=r. We now have x=12, y=5 and r=13. sinθ= 5 13 , cosθ= 12 13 , secθ= 13 12 , cscθ= 13 5 and cotθ= 12 5 .


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