-Given the function value and the quadrat restiction, find theta. csc theta= -1.

Question

-Given the function value and the quadrat restiction, find theta.

csc theta= -1.0306, interval (180 degrees, 270 degress)

theta= ___degrees

-In a circle with a 100 in radius, how long is an arc associated with an angle of 2.4 radians?

How long is an arc associated with an angle of 2.4 radians.

s=___in (round to nearest tenth)

-The planet Neptune has a radius of 15000 miles and rotates one revolution every 18 hours. What is the linear speed of a point on its equator, in mph?

The linear speed is approximately ___ miles per hour.

Explanation / Answer

Question 1:

the theta should be between pi and 1.5pi

now cosec theta = -1.0306

thus sin theta = -0.97

theta = -75 degrees

thus theta = -5pi/6

thus adding 2pi to it we get theta = 7pi/6 which is between pi and 1.5pi

Question 2:

s = theta x pi x r/180 = 4.2

Question 3:

1 rev/18hrs = 6.28rad/18hr = 0.349rad/hr

(linear speed) v = rw = 15000 x 0.349 = 5235 miles/hr

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