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Welcome! The Topic For Today Is…. Trigonometric Functions . 6.1: 200. Question: Convert each angle from degree to radians: 20  225 Answer /9 5/4 . Back. 6.1: 400. Question: Convert each angle from radians to degrees: 5 /6 1.75 radians Answer 150  100.3. Back.

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Welcome the topic for today is

Welcome!

The Topic For Today Is…


Trigonometric functions

Trigonometric Functions


6 1 200

6.1: 200

  • Question:

  • Convert each angle from degree to radians:

    • 20

    • 225

  • Answer

  • /9

  • 5/4

Back


6 1 400

6.1: 400

  • Question:

  • Convert each angle from radians to degrees:

    • 5/6

    • 1.75 radians

  • Answer

  • 150

  • 100.3

Back


6 1 600

6.1: 600

  • Question:

  • Determine the measure of the central angle that is formed by an arc length of 5cm in a circle with a radius of 2.5cm.

  • Answer

  • 2 radians

Back


6 1 800

6.1: 800

  • Question:

  • Determine the arc length of a circle with a radius of 8cm if the central angle is 300.

  • Answer

  • 40/3cm or 41.89cm

Back


6 1 1000

6.1: 1000

  • Question:

  • A Ferris wheel with diameter 84 m completes one revolution every 12 minutes.

    • Find the angular velocity, , in radians per second.

    • How far has the rider traveled 5 minutes into the ride.

  • Answer

  • 0.00873 radians/second

  • 110m

Back


6 2 200

6.2: 200

  • Question:

  • For the trigonometric ratio, determine in which quadrant the terminal arm of the principle angle lies:

    • sin 3/4

  • Answer

  • Second Quadrant

Back


6 2 400

6.2: 400

  • Question:

  • Determine the exact value of the trigonometric ratio:

    • csc 5/6

  • Answer

  • 2

Back


6 2 600

6.2: 600

  • Question:

  • For the following value of cos, determine the radian value of  if 2:

  • Answer

  • 5/4

Back


6 2 800

6.2: 800

  • Question:

  • The following point lies on the terminal arm of an angle in standard position: (-12, -5).

    • Determine the value of r.

    • Calculate the radian value of .

  • Answer

  • r = 13

  • 3.54 radians

Back


6 2 1000

6.2: 1000

  • Question:

  • A leaning flagpole, 5m long, makes an obtuse angle with the ground. If the distance from the tip of the flagpole to the ground is 3.4m, determine the radian measure of the obtuse angle.

  • Answer

  • 2.39 radians

Back


6 3 6 4 200

6.3&6.4: 200

  • Question:

  • State the period, amplitude, horizontal translation, and equation of axis for the following trigonometric function:

    • y = 5cos(-2x + /3)-2

  • Answer

  • Period: 

  • Amplitude: 5

  • Horizontal Translation: /6

  • Equation of Axis: y = -2

Back


6 3 6 4 400

6.3&6.4: 400

  • Question:

  • With a parent function of f(x)= sin x, determine the equation of a graph that has a period of  and an amplitude of 25. The equation of axis is y= -4.

  • Answer

  • y = 25sin(2x)-4

Back


6 3 6 4 600

6.3&6.4: 600

  • Question:

  • State the transformations that were applied to the parent function f(x) = sin x to obtain each of the following transformed functions:

    • f(x)= -sin(1/4x)

    • f(x)= sin(x - )-1

  • Answer

  • Reflection in the x-axis

  • Horizontal Stretch by a factor of 4

  • Horizontal Translation  units right

  • Vertical Translation 1 unit down

Back


6 3 6 4 800

6.3&6.4: 800

  • Question:

  • Sketch the graph for 0  x  2

    • y = 3sin(2(x - /6))+1

  • Answer

  • Expert will show graph to people that need it, on paper

Back


6 3 6 4 1000

6.3&6.4: 1000

  • Question:

  • Each person’s blood pressure is different, but there is a range of blood pressure values that is considered healthy. The function P(t)=-20cos(5/3t)+115 models the blood pressure, p, in millimeters of mercury, at time t, in seconds, of a person at rest.

    • What is the period of the function?

    • How many times does this person’s heart beat each minute?

  • Answer

  • Period: 6/5

  • 95 times

Back


6 5 6 6 200

6.5&6.6: 200

  • Question:

  • A cosine curve has an amplitude of 3 units and a period of 3 radians. The equation of the axis is y = 2, and a horizontal shift of /4 radians to the left has been applied. Write the equation of this function.

  • Answer

  • y= 3cos(2/3(x + /4))+ 2

Back


6 5 6 6 400

6.5&6.6: 400

  • Question:

  • Anup is waving a sparkler in a circular motion at a constant speed. The tip of the sparkler is moving in a plane that is perpendicular to the ground. The height of the sparkler above the ground, as a function of time, can be modeled by a sinusoidal function. At t = 0, the sparkler is at its highest point above the ground.

    • What does the amplitude of the sinusoidal function represent in this situation?

    • What does the period of the sinusoidal function represent in this situation?

  • Answer

  • Radius of circle

  • Time it takes the sparkler to complete on circle

Back


6 5 6 6 600

6.5&6.6: 600

  • Question:

  • Find an expression that describes the location of the vertical asymptote, for y = cot x, where nI and x is in radians.

  • Answer

  • tn= n nI

Back


6 5 6 6 800

6.5&6.6: 800

  • Question:

  • Graph y = csc x and y = sec x, for which values of the independent variable do the graphs intersect?

  • Answer

  • /4 and 3/4

Back


6 5 6 6 1000

6.5&6.6: 1000

  • Question:

  • To test the resistance of a new product to temperature changes, the product is placed in a controlled environment. The temperature in this environment, as a function of time, can be described by a sine function. The maximum temperature is 120C, the minimum temperature is -60C, and the temperature at t=0 is 30C. it takes 12 hours for the temperature to change from maximum to the minimum. If the temperature is initially increasing, what is the equation of the sine function that describes the temperature in this environment?

  • Answer

  • y = 90 sin(/12x) + 30

Back


6 5 6 7 200

6.5&6.7: 200

  • Question:

  • Graph y= csc x

  • Answer

  • Displayed on chalk board

Back


6 5 6 7 400

6.5&6.7: 400

  • Question:

  • Determine AROC of y=2cos(x - /2) +1 for:

    • 0 <x< /2

    • /6 <x< /2

  • Answer

  • 0.465

  • 0

Back


6 5 6 7 600

6.5&6.7: 600

  • Question:

  • What is the AROC of y=1/4cos(8x) +6 over the interval /4 <x< 

  • Answer

  • 0

Back


6 5 6 7 800

6.5&6.7: 800

  • Question:

  • State an interval where the function y=3cos(4x)-4 has a AROC that is:

    • Zero

    • Negative

  • Answer

  • 0 <x< /2

  • 0<x< /4

Back


6 5 6 7 1000

6.5&6.7: 1000

  • Question:

  • The height of the tip of an airplane propeller above the ground once the airplane reaches full speed can be modeled by a sin function. At full speed the propeller makes 200 revolutions per second. At t=0, the tip of the propeller is at its minimum height above the ground. Determine if IROC at t=1 is positive negative or zero

  • Answer

  • Zero

Back


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