Expert: Sherman D. - 5/2/2005

Question
Determine the exact values of the six trigometric functions of the angle 0 (with theline through it)

2.In the circle the angle has two points one is (12/13, 5/13) the other line lies on the line of x.


Find the point (x,y) n the unit circle that corresponds to the real number t

6. t=pi/3

10. t=5pi/3


evaluate (if possible) the sine, cosine, and tangent of the real number

14. t=pi/3

18. t= -4pi/3

22. t= -2pi

evaluate(if possible) the six trigometric functions of the real number

26.t=3pi/2


evaluate the triometricfunction using its period as an aid.

30. Cos 5pi

34.sin 19pi/6

use the value of the trigometric function toevaluate the indicated functions.

38. Sin(-t)=3/8
   (a) sin t
   (b) csc t

42. cos t= 4/5
   (a) cos (pi-1)
   (b) cos (t+pi)

use the calculator to evaluate the expression. Round to four decimal places.

46. cot 1

50. sec 1.8

True or False, determine whether the statement is true or false.Justify your answer.

59. Because sin(-t) = -sin t, it can be said taht the sine of a negative angle is a negative number.

60. tan a = tan(a-6pi)

Answer
2.) This one i can't really do.

Find the point (x,y) n the unit circle that corresponds to the real number t

If by this you mean the 6 trig functions, then

6.)
t = pi/3

sin(pi/3) = (sqrt(3))/2
cos(pi/3) = (1/2)
tan(pi/3) = sqrt(3)
sec(pi/3) = 2
csc(pi/3) = 2/(sqrt(3))
cot(pi/3) = 1/(sqrt(3))

10.)
t = 5pi/3

sin(5pi/3) = -(sqrt(3))/2
cos(5pi/3) = (1/2)
tan(5pi/3) = -sqrt(3)
csc(5pi/3) = -2/(sqrt(3))
sec(5pi/3) = 2
cot(5pi/3) = -1/(sqrt(3))


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14.)
t = pi/3

sin(pi/3) = (sqrt(3))/2
cos(pi/3) = (1/2)
tan(pi/3) = sqrt(3)

18.)
t = -4pi/3
sin(-4pi/3) = (sqrt(3))/2
cos(-4pi/3) = (-1/2)
tan(-4pi/3) =

22.)
t = -2pi
sin(-2pi) = 0
cos(-2pi) = 1
tan(-2pi) = 0

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26.)
t = 3pi/2

sin(3pi/2) = -1
cos(3pi/2) = 0
tan(3pi/2) = Uknown
sec(3pi/2) = Uknown
csc(3pi/2) = -1
cot(3pi/2) = 0

Unknowns occur when you have (1/0), but the inverse, which gives you (1/(1/0)) = (1/1)/(1/0) = (1/1)*(0/1) = 0

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30.) Cos 5pi = -1

34.) sin 19pi/6 = -.5

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38.)
Sin(-t)=3/8
inverse sin both sides
-t = .384396774
divide both sides by -1
t = -.384386774

(a) sin t = sin(-.3844) = (-3/8)
(b) csc t = 1/(sin(-.3844)) = -2.6015

42.)
cos t= 4/5
inverse cos both sides
t = .643501108

(a) cos (pi - 1), no "t" on this problem

(b) cos (t + pi) = cos(.6435 + pi) = -.8

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46.) cot 1 = 1/(tan(1)) = 57.2900

50.) sec 1.8 = 1/(cos(1.8)) = 1.0005

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If you go to www.quickmath.com, it will let you know if they are always true or not, and if not, it will either give you an answer or it won't be able to find any answers.

59.) True
60.) True