Trigonometry Practicie Test: Pre-AP Period____

Name___________________________________

Use the Pythagorean Theorem to find the length of the missing side.Then find the indicated trigonometric function ofthe given angle. Give an exact answer with a rational denominator.

1) Find sin !.

7

3

1)

2) Find cot !.8

7

2)

Use the special triangles to evaluate the expression. Rationalize all denominators.3) cos 30° 3)

4) tan "6

4)

5) cot "4

5)

Use an identity to find the value of the expression. Do not use a calculator.6) sin2 50° + cos2 50° 6)

Find a cofunction with the same value as the given expression.7) sin 69° 7)

Use a calculator to find the approximate value of the expression. Round the answer to two decimal places.8) cos 4° 8)

Convert the angle in degrees to radians. Express answer as a multiple of !.9) 150° 9)

10) - 105° 10)

1

Convert the angle in radians to degrees.

11) - "2

11)

12) 1112" 12)

Draw the angle in standard position. Label the reference angle (if possible) and its value.

13) 2"3 13)

14) 13"6 14)

15) - 7"6

15)

16) 270° 16)

17) -150° 17)

Find a positive coterminal angle and a negative coterminal angle that is different than the given angle.18) -35° 18)

19) 365° 19)

20) 7"3 20)

21) - 2"7

21)

Find the length of the arc on a circle of radius r intercepted by a central angle ". Round answer to two decimal places.

22) r = 15.26 inches, ! = 5"3

22)

23) r = 2 yards, ! = 55° 23)

Evaluate the trigonometric function at the quadrantal angle, or state that the expression is undefined.

24) sin 3"2

24)

25) sec " 25)

Let " be an angle in standard position. Name the quadrant in which the angle " lies.26) tan ! < 0, sin ! < 0 26)

2

27) cos ! > 0, csc ! < 0 27)

Find the exact value of the indicated trigonometric function of ".

28) csc ! = - 32, ! in quadrant III Find cot !. 28)

29) tan ! = 724 , 180°< ! < 270° Find cos !. 29)

30) cos ! = 23, tan ! < 0 Find sin !. 30)

Use reference angles to find the exact value of the expression. Do not use a calculator.

31) tan -3"4

31)

32) csc 5"3

32)

33) cot -11"6

33)

Solve the problem.34) A straight trail with a uniform inclination of 11° leads from a lodge at an elevation of 800

feet to a mountain lake at an elevation of 5700 feet. What is the length of the trail (to thenearest foot)?

34)

35) A building 230 feet tall casts a 50 foot long shadow. If a person looks down from the topof the building, what is the measure of the angle between the end of the shadow and thevertical side of the building (to the nearest degree)? (Assume the person's eyes are levelwith the top of the building.)

35)

36) A forest ranger looking out from a ranger's station can see a forest fire at a 35° angle ofdepression. The ranger's position is 100 feet above the ground. How far is it from thebase of the ranger's station to the fire. If necessary, round the answer to two decimalplaces.

36)

37) A building 240 feet tall casts a 100 foot long shadow. If a person stands at the end of theshadow and looks up to the top of the building, what is the angle of the person's eyes tothe top of the building (to the nearest hundredth of a degree)? (Assume the person's eyesare 5 feet above ground level.)

37)

38) A surveyor is measuring the distance across a small lake. He has set up his transit onone side of the lake 130 feet from a piling that is directly across from a pier on the otherside of the lake. From his transit, the angle between the piling and the pier is 55°. Whatis the distance between the piling and the pier to the nearest foot?

38)

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Answer KeyTestname: PRACTICETEST.AP

1) 7 5858

2) 78

3) 32

4) 33

5) 16) 17) cos 21°8) 1.00

9) 5"6 radians

10) - 7"12

radians

11) -90°12) 165°13)

14)

15)

16)wrong

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Answer KeyTestname: PRACTICETEST.AP

17)

18) 325°19) 5°

20) "3

21) 12"722) 79.90 inches23) 1.92 yards24) -125) -126) quadrant IV27) quadrant IV

28) 52

29) - 2425

30) - 53

31) 1

32) - 2 33

33) 334) 25,680 feet35) 12°36) wrong37) 66.95°38) 186 feet

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