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Exam 7: Trigonometry and Periodic Functions

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Question 51

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Find the area of the triangle given if $c=6$ and $A=38^{\circ}$ . Give your answer correct to 3 decimal places.

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Question 52

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Suppose the table below is for a periodic function $f$ with period 3: What is the next integer value $n$ at which $f(n)=1$ ?

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Question 53

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Is the period of $\cos (x /4)$ greater than, less than, or the same as the period of $\tan (x / 8)$ ?

Find the reference angle for $\frac{5 \pi}{6}$ radians.

Suppose you are on a ferris wheel (that turns in a counter clockwise direction) and that your height, in meters, above the ground at time $t$ , in minutes, is given by $h(t)=17 \sin \left(\frac{\pi}{2} t\right)+18$ . How many meters is the radius of the wheel?

A vacationer sits all day on the corner of a pier in Boston Harbor and notices that at 9 am, when the water level is at its lowest, the water's depth is 2.5 feet. At $4 \mathrm{pm}$ , the water has risen to its maximum depth of 10.5 feet. If the depth of the water level varies periodically, let $f(t)$ be the formula for the depth of the water, in feet, as a function of time $t$ , in hours past 9 am. What is the period of the graph of $f(t)$ ?

Find the reference angle for $343^{\circ}$ .

Point A lies on a circle of radius 3 at angle $26^{\circ}$ . Point $B$ lies on a circle of radius 4 at angle $119^{\circ}$ . If both circles are centered at the origin, what is the distance between the two points? Round your answer to 2 decimal places.

Find the coordinates of the point on the unit circle with angle $\alpha$ if $\sin \alpha=0.640$ . Round each coordinate to 3 decimal places.

Which is larger: $\sin \left(\frac{3 \pi}{7}\right)$ or $\cos \left(\frac{3 \pi}{7}\right)$ ?

Find the following exactly using the figure given if $a=4$ and $b=5$ . Express your answers as unsimplified radicals when appropriate. A) $\sin A^{\circ}$ B) $\cos A^{\circ}$ C) $\tan A^{\circ}$ D) $\sin B^{\circ}$ E) $\cos B^{\circ}$ F) $\tan B^{\circ}$

Select the graph of $-2+\tan (-2 \theta)$ .

The number $(\sin (10 \mathrm{rad}))(\cos (7 \mathrm{rad}))$ is positive.

A circle of radius 3 is centered at the origin. Point A lies on the circle at angle $201^{\circ}$ . Point $\mathrm{B}$ lies outside the circle and has coordinates $(5,-2)$ . What is the distance between these two points? Round your answer to 2 decimal places.

The number of tourists (in thousands) visiting a certain beach can be approximated by the formula $f(t)=17+6 \sin (30 t)$ , where $t$ is the number of months after January 2007 . Find the maximum and minimum number of tourists who visit this beach at one time.

The midline of the periodic function shown below is $y=$ ------------

There is a red dot on the outer edge of a wheel. The wheel is rolling on the ground in a counterclockwise direction and has diameter 17 inches. Find a formula using the sine function for the height of the dot above ground level after $t$ seconds if the wheel completes one full revolution every 2 seconds. At $t=0$ the dot in 9 o'clock position.

There is a red dot on the outer edge of a wheel. The wheel is rolling on the ground in a counterclockwise direction and has diameter 13 inches. Which of the following is a formula using the sine function for the height of the dot above ground level after $t$ seconds if the wheel completes one full revolution every 2 seconds. At $t=0$ the dot in 9 o'clock position.

Suppose the table below is for a periodic function $f$ with period 3: Evaluate $f(86)$ .

The coordinates of the point on the unit circle at the angle $330^{\circ}$ are $(\ldots, \ldots)$ . Round each coordinate to 3 decimal places.