Transformations and Periodic Function

Find Sin angle A

B. 4/5

find sin A

B. 4/5

find sin L

B. 5/13

find the sine and cosine of 30 degrees

B. sin 30 = 1/2, cos 30 = /3/2

find sin 60 degrees

C. /3 / 2

given that cos (X) = 1/3 find sin ( 90 - x)

1/3

Given that sin (x) = 7/11 find cos (90-x)

7/11

1. Reflect the triangle across the y-axis. 2. Reflect the image across the x-axis. The final image is the same as what single transformation?

a 180° rotation about the origin

B. /2 / 2

find sin 45 degrees

Triangle MNO is rotated 180 degrees using the origin as the center of rotation. Which sequences of transformations will produce the same results? Check all that apply.

- a reflection over the x-axis and then a reflection over the y-axis - a reflection over the y-axis and then a reflection over the x-axis

The displacement, d, in millimeters of a tuning fork as a function of time, t, in seconds can be modeled with the equation d=0.4sin(1760pit). What is the maximum displacement of the tuning fork?

0.4 mm

The height, h, in feet of the tip of the minute hand of a wall clock as a function of time, t, in minutes can be modeled by the equation h= 0.75 cos ( pi/ 30(t-15))+8. Which number (from 1 to 12) is the minute hand pointing to at t = 0?

9

The height, h, in feet of a flag on one blade of a windmill as a function of time, t, in seconds can be modeled by the equation h=3sin(4pi/5(t-1/2))+12. What is the minimum height of the flag?

9 feet

The equation h= 7sin ( pi / 21t) can be used to model the height, h, in feet of the end of one blade of a windmill turning on an axis above the ground as a function of time, t, in seconds. How long is the blade? Assume that the blade is pointing to the right, parallel to the ground, at t = 0, and that the windmill turns counterclockwise at a constant rate.

A. 7 feet

find TAN C

C. 12/5

Ethan created three triangles: triangle X, triangle Y, and triangle Z.

C. Triangles X and Z are congruent.

A buoy starts at a height of 0 in relation to sea level and then goes up. Its maximum displacement in either direction is 6 feet, and the time it takes to go from its highest point to its lowest point is 4 seconds. Which of the following equations can be used to model h, the height in feet of the buoy in relation to sea level as a function of time, t, in seconds?

C. h=6sin ( pi/ 4 t)

5/13

Find cos C

4/3

Find tan E

D. cos 60 = 1/2 tan 60 = /3

Find the cosine and tangent of 60 degree

Mrs. Hamilton shows her students this graph and asks them to determine how figure A was transformed to figure B. Marcus suggests that figure A was reflected over the y-axis and then translated 2 to the right and 1 up. Julianne agrees, and states that the transformations could happen in any order. Which best describes the accuracy of Julianne's statement?

Inaccurate. A translation of 2 to the right and 1 up and then a reflection over the y-axis results in a figure that is located in the second quadrant

If the sine of angle A is 3/5 and the cosine of angle A is 4/5, explain how to find the tangent of A.

Since sine is defined as opposite over hypotenuse, the length of the opposite side is 3, and the length of the hypotenuse is 5. Since cosine is defined as adjacent over hypotenuse, the length of the adjacent side is 4. Tangent is the ratio of the opposite side over the adjacent side, so the tangent is 3/4.

Triangle MNO is reflected over the x-axis and then translated up 4 and right 3. How can the transformation be amended such that the translation can occur before the reflection and have the image remain in the same position?

Translate the pre-image down 4 and right 3 and then reflect the figure over the x-axis

Sin (J) = Cos (L)

Which of the following statements is true?

Figure G is rotated 90 degrees clockwise about the origin and then reflected over the x-axis, forming figure H. Which sequence of transformations will produce the same results?

a reflection over the y-axis and then a rotation 90 degrees clockwise about the origin

Figure X is translated down 5 and then reflected over the y-axis, forming figure Y. Which sequence of transformations results in the same transformation?

a reflection over the y-axis and then a translation down 5 unit

Which of the following ratios is used in finding the sine of an angle in a right triangle?

opposite leg/ hypotenuse

Triangle ABC is shown with four images that are each the result of a transformation of triangle ABC. For which triangle is one reflection necessary for the transformation to occur?

triangle GHI

EF

which side is opposite 0

Find a possible solution to the equation cos ( x+2) = sin (3x)

x= 22 degrees

3/5

Find cos c

DE/DF

Find sin (0)

The vertices A(-2, -1), B(-3, 2), C(-1, 3), and D(0, 0) form a parallelogram. The vertices A'(-1, -2), B'(2, -3), C'(3, -1), and D'(0, 0) are the image of the parallelogram after a sequence of transformations. Which sequence of transformations could produce the image from the pre-image?

NOT a 90 degree counterclockwise rotation about the origin and then a reflection over the x-axis

Which of the following situations can be modeled with a periodic function?

the height of a pebble stuck in the tread of a tire

Suppose that you want to model the height of a rider on a Ferris wheel as a function of time. The amplitude of the function you use as a model should be equal to which of the following?

the radius of the Ferris wheel

Figure A is translated 3 units right and 2 units up. The translated figure is labeled figure B. Figure B is reflected over the x-axis. The reflected figure is labeled figure C. Which best explains why figure A is congruent to figure C?

A. A = B and B = C

Which leg is adjacent to 0?

B. ED

Jason states that ABC = RST . Kelley states that ABC = TSR Which best describes the accuracy of the congruency statements?

Both statements could be correct. RST could be the result of two translations of ABC. TSR could be the result of a reflection and a translation of ABC

Triangle GHI is rotated 90mc002-1.jpg clockwise and then reflected over the y-axis. Which congruency statement is true?

C. triangle GHI = triangle G'' H'' I''

The height, h, in feet of a buoy in relation to sea level as a function of time, t, in seconds can be modeled by the graph below. How long does it take for the buoy to go from its highest point to its lowest point and then back to its highest point?

D. 4 seconds

3/5

Find sin NOM

A teacher asks students to determine the accuracy of this statement. A reflection over the x-axis and then over the y-axis results in the same transformation as a 180 degrees rotation about the origin of the original figure. Kwame's explanation of the accuracy of the statement is shown below. Step 1: Choose the vertices of a pre-image: (1, 2), (1, 4), (2, 3). Step 2: Reflect the pre-image over the x-axis: (1, -2), (1, -4), (2, -3). Step 3: Reflect the figure from step 2 over the y-axis: (-1, 2), (-1, 4), (-2, 3). Step 4: Rotate the pre-image 180 degrees : (-1, -2), (-1, -4), (-2, -3). Step 5: Compare the reflected figure to the rotated figure. The vertices are not located in the same place, therefore the statement made by the teacher is inaccurate. Which best explains Kwame's solution?

Kwame's explanation and solution are incorrect. He reflected the pre-image at step 3, rather than the figure from step 2.

Square ABCD is shown with four congruent images such that ABCD = FGHI = JKLM = NOPQ = RSTU For which square is a reflection necessary to produce the transformed figure?

RSTU

Which of the following ratios is used in finding the tangent of an angle in a right triangle?

opposite leg/adjacent leg