JPRaup said:
thanks for the help
now i need to determine the exact value of thes
1. sin 0
2. sin pi/2
3. sin 3pi/4
4. cos pi
5.cos 7pi/6
6. cos pi/3
7. tan 7pi/4
8. tan pi/6
9. tan 2pi/3
10. tan pi/2
11. cos((sin ^-1) 1/2)
12. sin ^-1 (sin 7pi/6)
ill try to edit the thread as a figure them out, but any help is appreciated
Do you need to know how to evaluate their specific values, or just how to come across them?
Basically, these are the simplest trig identities. Multiples of 90 degrees will have values of either 0 or +1/-1
Sin 0 = 0
Sin 90 = 1
Sin 180 = 0
Sin 270 = -1
Cos 0 = 1
Cos 90 = 0
Cos 180 = -1
Cos 270 = 0
Sin 30 = .5
Sin 60 = .5sqrt(3)
Sin 45 = sqrt(.5)
Cos 30 = sqrt(.5)
Cos 60 = .5
Cos 45 = sqrt(.5)
tan 0 = 0
tan 30 = 1/sqrt(3)
tan 45 = 1
tan 60 = sqrt(3)
tan 90 = undefined
and so on, bearing in mind the quadrant rule:
In the first quadrant of a circle (0.0 -90 degrees, top right quarter), sin cos and tan are all positive.
In the second quadrant of a circle (90.0 -180 degrees, top left quarter), sin alone is positive.
In the third quadrant of a circle (180.0 - 270 degrees, bottom left quarter), tan alone is positive.
In the fourth quadrant of a circle (270.0 - 0 degrees, bottom right quarter), cos alone is positive.
360 degrees is 2pi radians, making 90 degrees pi/2, 60 degrees pi/3 etc etc
sin^-1 works in the opposite sense, in the way that log works in the opposite sense of exponential:
sin pi/2 = sin 90 = 1
therefor
sin^-1 = pi/2 = 90
therefor
1. sin 0 = 0
2. sin pi/2 = sin 90 = 1
3. sin 3pi/4 = sin 135 = sqrt(.5) (sin 45 in the second quadrant)
4. cos pi = cos 180 = -1
5.cos 7pi/6 = cos 210 = -.5sqrt(3) (cos 20 in the third quadrant)
6. cos pi/3 = cos 60 = .5
7. tan 7pi/4 = tan 315 = -1 (tan 45 in the fourth quadrant)
8. tan pi/6 = tan 30 = 1/sqrt(3)
9. tan 2pi/3 = tan 120 = - 1/sqrt(3) (tan 30 in the second quadrant)
10. tan pi/2 = tan 90 = undefined (infinity)
11. cos((sin ^-1) 1/2) = cos pi/6 = cos 30 = .5sqrt(3)
12. sin ^-1 (sin 7pi/6) = 7piu/6 = 210 degrees
