sin(x) sin(x) sin(x) sin(x x x) 17 β = arcsin ( ) 15 β = arcsin ( ) o

Transcription

1 Math 104 Trigonometr Practice Eam 1 name: 1 A B C D E F G H I Select epressions equivalent to: sin 3 () Select epressions equivalent to: sin() sin() sin() sin( ) (sin()) 3 A B C D E F G H I Which epression describes the measurement of the angle below: 17 β = arcsin ( ) 1 17 β = arccos ( ) o 1 C) 1 β = arcsin ( ) o 17 daabz.com Math 104 Trigonometr Practice Eam 1 page 1/1

2 3 A B C D E F G H I based on the diagram, select the true statement/s tan ( 60 o 3 1 tan ( 30 o 1 3 cos ( 60 o 3 sin ( 30 o 1 E) sin ( 60 o 3 F) G) tan ( 30 o 3 1 cos ( 30 o 1 H) cos ( 30 o 3 I) tan ( 60 o A B C D E F G H I Negative Angles are b definition, drawn A) counter-clockwise B) clockwise counter-clockwise - 0 clockwise - daabz.com Math 104 Trigonometr Practice Eam 1 page /1

3 A B C D E F G H I Select an and all true statement/s in reference to the diagram below. Approimations are acceptable where appropriate. B = 6 cos 6 o =.371 = sin 6 o G) H) = 6 cos 6 o B = 90 o 6 o.4378 B = arcsin ( ) B = 180 o B.4378 B = arccos ( ) o 6 A B C D E F G H I based on the diagram, select the true statement/s sin ( 30 o 3 sin ( 60 o 3 cos ( 60 o 3 tan ( 60 o 3 1 cos ( 60 o 1 tan ( 30 o 1 3 G) H) tan ( 60 o 1 3 cos ( 30 o 1 daabz.com Math 104 Trigonometr Practice Eam 1 page 3/1

4 7 A B C D E F G H I Suppose we know triangle and θ Select the true statement/s is an interior angle of a right cos (θ tan (θ 4 9 cos (θ sin (θ 4 4 tan (θ E) 9 sin (θ A B C D E F G H I consider the sides and ratio given below: b.177 h h h 3.13 b 3.64 b.69 G) not enough information H) none of these daabz.com Math 104 Trigonometr Practice Eam 1 page 4/1

5 9 A B C D E F G H I Select an and all true statement/s in reference to the diagram below. Approimations are acceptable where appropriate. = C) B = arcsin ( ) D) = cos 46 o E) B = 180 o B B = arccos ( ) B 46 o 10 A B C D E F G H I Select epressions equivalent to: sin( + ) none of these sin() + sin() 11 A B C D E F G H I Reference Angles are b definition, drawn STARTING FROM which side A) positive Y ais B) negative X ais negative,x pos,y - 0 positive,x X C) positive ais - negative,y daabz.com Math 104 Trigonometr Practice Eam 1 page /1

6 1 A B C D E F G H I Suppose on our drive to Vegas ou see an object in the far distance. You stick our handout and point at it, and keep our arm fied and frozen. Suppose 6 miles later ou pass the object at a perpendicular distance to the road, then another 6 miles later ou stick out our other arm and point at the object (with our unfrozen arm). Suppose now ou observe the angle ou have created with our arms to be 1 o. How far is the object from the road? [hint: draw our arms as if the were ver ver long ] A) not enough information given B) = miles = miles = miles = 4.74miles = miles G) none of these 1 o 6 miles 6 miles 13 A B C D E F G H I consider the sides and ratio given below: A) not enough information B) h 14.0 b 9.37 h 8.30 b 4 b h G) H) none of these daabz.com Math 104 Trigonometr Practice Eam 1 page 6/1

7 14 A B C D E F G H I Suppose we know Select the true statement/s cos (β sin (β 6 11 sin (β 6 11 C) D) E) 11 tan (β cos (β 6 6 tan (β A B C D E F G H I A) if instead of 10 triangles we cut out 104 triangles, π the sum of their area would be sin ( ) 104 θ B) if instead of 10 triangles we cut out 104 triangles, 1 π the sum of their area would be sin ( ) 104 C) the sum of the area of the triangles is 1 π 10 1 sin ( ) 10 D) angle θ = π 10 Assume the circle has radius 1, and all 10 triangles are congruent. E) the area of each triangle is F) with base 1, the height of each triangle is 1 π 10 1 sin ( ) π sin ( ) 10 G) the longer side of each triangle is 1 H) angle θ = π 10 I) with base 1, the height of each triangle is π sin ( ) 10 daabz.com Math 104 Trigonometr Practice Eam 1 page 7/1

8 16 A B C D E F G H I Select an and all true statement/s in reference to the diagram below. Approimations are acceptable where appropriate A) B = arccos ( ) B) C) = D) E) = cos 60 o = cos 60 o = sin 60 o B 60 o daabz.com Math 104 Trigonometr Practice Eam 1 page 8/1

9 17 A B C D E F G H I Select an and all true statement/s in reference to the diagram below. Approimations are acceptable where appropriate. A) [tan ( 41 o ) tan ( 6 o )] = 4 tan ( 6 o ) B) C) = ( + 4)tan ( 6 o ) =.46 D) tan ( 41 o ) tan ( 6 o 4 tan ( 6 o ) = tan ( 41 o ) tan ( 6 o ( + 4)tan ( 41 o ) G) H) = ( + 4)tan ( 41 o ) = 4 tan ( 6 o ) tan ( 41 o ) tan ( 6 o ) 6 o 4 41 o I) none of these daabz.com Math 104 Trigonometr Practice Eam 1 page 9/1

10 18 A B C D E F G H I Solve the triangle completel. Then use our solution to select an and all true statement/s in reference to the diagram below. Approimations are acceptable where appropriate. z = cos 3 o = = z cos 3 o B = arccos ( ) z G) H) I) = z sin 3 o B = arcsin ( ) B = o z = z = tan 3 o B z 3 o daabz.com Math 104 Trigonometr Practice Eam 1 page 10/1

11 19 A B C D E F G H I Suppose on a nice december evening ou gaze upon our favorite star. You stick our handout into the sk and point at it, then ou keep our arm fied and frozen. Until 6 months later when ou reach for the sk again and point at our star with our other arm. Suppose now ou observe the angle ou have created with our arms to be 0.13 o. How far is the star from the sun? [hint: assume the earth orbits in a circular motion around the sun once ever 1 month, where r = km the orbit has radius of ] A) = km B) not enough information given = km = km E) none of these 0.13 o r daabz.com Math 104 Trigonometr Practice Eam 1 page 11/1

12 0 A B C D E F G H I based on the diagram, select the true statement/s cos (α z cos (α v tan (β v z sin (β z sin (β v sin (α z G) H) tan (α v z sin (α v 1 A B C D E F G H I Select an and all true statement/s in reference to the diagram below. Approimations are acceptable where appropriate. A) [tan ( 46 o ) tan ( 33 o )] = 10 tan ( 33 o ) B) = ( + 10)tan ( 33 o ) C) tan ( 46 o ) tan ( 33 o 10 tan ( 33 o ) D) tan ( 46 o ( + 10)tan ( 33 o ) tan ( 33 o ( + 10)tan ( 46 o ) = G) 33 o o tan ( 46 o tan ( 33 o ) + 10 tan ( 33 o ) H) I) none of these = 10 tan ( 33 o ) tan ( 46 o ) tan ( 33 o ) daabz.com Math 104 Trigonometr Practice Eam 1 page 1/1

13 A B C D E F G H I 8 α 13 4 α = sin 1 4 ( ) 8 α = sin 1 8 ( ) 4 α 7.08 o α 1.6 o Consider the following belt-pulle sstem. Assume the indicated radius segment is perpendicular to the direction of the portion of the belt that does not touch the pulle. Find the angle. α α.0 o α = cos 1 8 ( ) 13 3 A B C D E F G H I Which epression describes the measurement of the angle below: A) 17 β = arccos ( ) o 1 B) 1 β = arctan ( ) o 17 C) 1 β = arccos ( ) o 17 daabz.com Math 104 Trigonometr Practice Eam 1 page 13/1

14 4 A B C D E F G H I Select an and all true statement/s in reference to the diagram below. Approimations are acceptable where appropriate. = cos 46 o = B = 180 o B B = arcsin ( ) E) B = arccos ( ) F) 6 G) = B = 90 o 46 o B 6 46 o A B C D E F G H I Positive Angles are b definition, drawn A) counter-clockwise B) clockwise counter-clockwise - 0 clockwise - daabz.com Math 104 Trigonometr Practice Eam 1 page 14/1

15 1) A,) C,3) ACDEH,4) B,) ABEH,6) BDEF,7) AE,8) AB,9) E,10) B,11) C,1) F,13) DG,14) AC,1) BCEFGH,16) B,17) ABDEH,18) ABDEFGHI,19) C,0) ADGH,1) ABCDFGH,) C,3) A,4) DFG,) A daabz.com Math 104 Trigonometr Practice Eam 1 page 1/1