tr-t1b-a

Suppose that in 20 seconds a central angle of 23

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An object is traveling around a circle with a radius of 20 meters. Suppose that in 20 seconds a central angle of 2/3 radian is swept out. What is the angular speed ω of the object, and what is the linear speed ν of the object? Here give the exact value of the item followed by its decimal approximation. ω = (1/30) radians/sec. .0333 radians/sec. ν = (2/3) meters/sec. .666 meters/sec. 7. (5 pts.) If θ is an acute angle, and cos( θ ) = 2/3, obtain the exact values for the remaining four ———— trigonometric functions. tan( θ )= 5 1/2 /2; cot( θ ) = 2/5 1/2 ; sec( θ ) = 3/2; csc( θ ) = 3/5 1/2 ; sin( θ )=5 1/2 /3 8. (5 pts.) If the point (-5, 4) is on the terminal side of an angle θ , obtain the exact value of each of the six trigonometric functions of θ . sin( θ ) = 4/(41) 1/2 ; cos( θ ) = -5/(41) 1/2 ; tan( θ ) = -4/5; cot( θ ) = -5/4; sec( θ ) = -(41) 1/2 /5; csc( θ ) = (41) 1/2 /4 9. (5 pts.) What is the reference angle θ r for an angle θ = -195°? θ r = 15°
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TEST-01b/MAC1114 Page 2 of 2 10. (5 pts.) Suppose cos θ = -(1/5) and tan θ > 0. What is the exact value of each of the remaining trigonometric functions? sec( θ ) = -5; tan( θ ) = (24) 1/2 ; sin( θ ) = -(24) 1/2 /5; csc( θ ) = -5/(24) 1/2 ; cot( θ ) = 1/(24) 1/2 ; 11. (18 pts.) Fill in the following table with the information requested concerning domain, range, and period. Function Name Domain (in radians) Range Period (in radians) cot( θ ) B, below. π sec( θ ) A, below. (- ,-1] [1, ) 2 π tan( θ ) A, below. π sin( θ ) [-1,1] 2 π cos( θ ) [-1,1] 2 π csc( θ ) B, below. (- ,-1] [1, ) 2 π A={x ε :x (2k + 1)( π /2), k any integer } B={x ε :x k π , k any integer } 12. (2 pts.) Use a calculator to obtain the approximate value of each of the following expressions. Round your answer to two decimal places. sin 10 -.54 sin 10° .17 13.,14.,15.: Partial graphs may be found in the text. They generally don’t show two periods that are symmetric with respect to the origin.
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Suppose that in 20 seconds a central angle of 23 radian is...

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