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Please I need help with my homework. Due date is September 1, 2016.


MATH 108 Fall 2016 Quiz 1

 

Problem 1. 2 pts. Convert 108° to radian measure. Leave your answer in terms of ?.

 


 

Problems 2 through 5. 1 pt. each. Find the exact value for each, if it exists. Finding an ?exact

 

value? means that decimal approximations from your calculator are not acceptable as answers.

 

2. cos(4?/3)

 


 

3. sin(-300°)

 


 

4. cot(3?/2)

 


 

5. sec(135°)

 


 

Problem 6. 5 pts. Prove the identity. Use algebra and basic trigonometric formulas to transform

 

one side of the equation to look like the other side. Show the whole process, without skipping

 

any steps, and explain what you are doing in each step.

 

Prove: sin2x ? tan2x = tan2x - sin2x

 


 

Problem 7. 3 pts. Solve, using a calculator.

 

A wheel with a 20 inch diameter is turning at the rate of 54 revolutions per minute. What is the

 

linear speed of a point on the rim, measured to the nearest inch per minute?

 


 

Problem 8. 5 pts. Find the exact values of the remaining 5 circular functions (sine, tangent,

 

cotangent, secant, and cosecant) for angle ?, given that cos? = 1/8 and ? is an angle in the 4th

 

quadrant. Find exact answers for this problem- no credit for approximations. Reduce any

 

fractions to lowest terms.

 


 

Problem 9. 4 pts. Solve, finding ALL solutions. Express your answer exactly, and in radians.

 

Solve sin ? =

 


 

Problems 10-11. 2 pts. each. Use a calculator to find the function values to four decimal places.

 

10. csc125°

 


 

11. tan(-5?/9)

 


 

Problem 12. 3 pts. Solve, using a calculator.

 

From a spot marked X, the angle of elevation to the top of a cliff is 29°24?. If the bottom of the

 

cliff is 1850 feet from spot X, how high is the cliff (to the nearest foot)? Assume that a right

 

triangle is formed.

 

Top of clif

 


 

1850 feet

 

X

 


 

Bottom of cliff

 


 

 







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