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Chapter 7: Q. 105 (page 475)

A searchlight at the grand opening of a new car dealership casts a spot of light on a wall located 75 meters from the searchlight. The acceleration r of the spot of light is found to be r=1200sec胃(2sec2胃-1). Show that this is equivalent tor=1200(1+sin2胃cos3胃)

Short Answer

Expert verified

The given expressions are equivalent.

Step by step solution

01

Step 1. Given Information

The given expressions arer=1200sec胃(2sec2胃-1)andr=1200(1+sin2胃cos3胃)

02

Step 2. Calculation

Consider one expression and prove it is equivalent to the other given expression.

1200sec胃(2sec2胃-1)=1200cos胃(2cos2胃-1)=1200cos胃(2-cos2胃cos2胃)=1200cos胃(1+1-cos2胃cos2胃)=1200cos胃(1+sin2胃cos2胃)=1200cos3胃(1+sin2胃)=r

Thus, we can conclude that the given expressions are equivalent.

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