The graph shows the average number of daylight hours per day in Los Angeles. The model has the form $$y=a\cos\left(bt\right)\degree+d$$ hours, where t is the time in months after January. 1). Find the vlaue of a, b and d. 2). Predict the average number of daylight hours in Los Angeles during September.

$$\left(1\right).\ a=-\frac{2}{5},\ b=30,\ d=12;\ \ \ $$ (2). 13.25 hours

$$\left(1\right).\ a=\frac{2}{5},\ b=30,\ d=12;\ \ \ $$ (2). 13.25 hours

$$\left(1\right).\ a=-\frac{2}{5},\ b=30,\ d=10;\ \ \ $$ (2). 12.25 hours

$$\left(1\right).\ a=-\frac{2}{5},\ b=30,\ d=12;\ \ \ $$ (2). 12.25 hours

The graph of $$y=p\cos qx+r,$$ for –5 ≤ x ≤ 14, is shown left. There is a minimum point at (0, –3) and a maximum point at (4, 7). (1) Find the value of p , q and r . (2). The equation y = k has exactly two solutions. Write down the value of k .

$$\left(1\right).p=-5,q=0.785\ $$ $$or\ \left(\frac{\pi}{4}\right),r=2;$$ (2). k=-3.

$$\left(1\right).p=5,q=0.785\ $$ $$or\ \left(\frac{\pi}{4}\right),r=2;$$ (2). k=-2.

$$\left(1\right).p=-5,q=1.05\ \ $$ $$or\ \left(\frac{\pi}{3}\right),r=2;$$ (2). k=-3.

$$\left(1\right).p=5,q=1.05\ \ $$ $$or\ \left(\frac{\pi}{3}\right),r=2;$$ (2). k=-2.

$$f\left(x\right)=5\cos\left(45x\right)\degree$$ ,Consider the graph of f(x) . Write down (i) the x -intercept that lies between x = 0 and x =3; (ii) the period; (iii) the amplitude.

(i) x -intercept = 2 (ii) period = 8 (iii) amplitude = 5

(i) x -intercept = 1.5 (ii) period = 8 (iii) amplitude = 5

(i) x -intercept = 1.5 (ii) period = 8 (iii) amplitude = -5

(i) x -intercept = 2 (ii) period = 8 (iii) amplitude = -5

Let $$f(t)=a\cos b(t-c)+d,t\ge0$$ . Part of the graph of y = f ( t ) is given.When t = 3, there is a maximum value of 29, at M. When t = 9 , there is a minimum value of 15. (1) Find the value of a, b , d . (2) Write down a value for c .

$$\left(1\right).\ a=7,b=\frac{\pi}{6},\ d=22$$ (2) c=3

$$\left(1\right).\ a=-7,b=\frac{\pi}{3},\ d=21$$ (2) c=9

$$\left(1\right).\ a=-7,b=\frac{\pi}{6},\ d=22$$ (2) c=3

$$\left(1\right).\ a=-7,b=\frac{\pi}{6},\ d=21$$ (2) c=9

IB AISL Math trigonometry

Authored by Max Power

Mathematics

11th Grade

CCSS covered

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MULTIPLE CHOICE QUESTION

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MULTIPLE CHOICE QUESTION

1 min • 3 pts

Find the sine function shown in this graph.

Find the unknowns in the function.

Find the unknowns in the funciton.

A steamroller has spot of paint on its roller. As the steamroller moves, the spot rotates around the axle. The roller has radius 1 meter and completes one full revolution every 2 seconds.
1). Construct a cosine model to describe the height of the paint spot over time.
2). Use your model to predict the height of the spot after 3.6 seconds.

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