Hey,
The unit circle will help you answer those.
cos(degree) is the x value
sin(degree) is the y value
so cos(270) = 0.
Does that make sense?
Assuming trigonometric arguments in degrees
1. -1/2
2. -sqrt3
3. 0
4. 1/2
5. complex infinity
6. (-sqrt3)/2
Assuming trigonometric arguments in radians
1. 0.46771...
or (I/2)/E^(210 I) - (I/2) E^(210 I)
2. 45.2447...
or (I (E^(-300 I) - E^(300 I)))/(E^(-300 I) + E^(300 I))
3. 0.98438...
or 1/(2 E^(270 I)) + E^(270 I)/2
4. -0.9524...
or 1/(2 E^(60 I)) + E^(60 I)/2
5. 0.935809...
or (I (E^(-450 I) - E^(450 I)))/(E^(-450 I) + E^(450 I))
6. 0.945445...
or (I/2)/E^(240 I) - (I/2) E^(240 I)
For more alternate forms, width/height triangles when using sin, cos, tan, properties, decimal approximations, or alternate/integral representations, go to wolframalpha.com that can solve all if not most equations, even for x. remember technology is your friend!
absolutely. Just go to that site like I said, and it makes one for you with height and length.
as for sinx=1
sin X=1 - Wolfram|Alpha
there ya go!
These are values to be memorized, using the unit circle.
You could use your calculator, 2nd function, then sine, then 1,then =. But,
sin 90 =1
cos 0 =1
tan 45 =1
In the unit circle, sine is 1at pi/2 (and all variations of it b y adding 2pi). So, when sin x = 1, x= pi/2 +2kpi where k is a constant.
Similarly, cos x = 1 at angle 0, 2pi, etc. 2pi + 2kpi for short.
Tanget is sin x / cos x. Therefore, tan x = 1 when sin x / cos x are equal (but different of 0).
heres another way of looking at it
on your calculator if you push second and then sin and then type in one it will give you the answer
it works the same way for cosine and tan
another way of thinking of it is that at what degree or radian will you get one
at ninety degrees or 1/2 pi the sin will be one
the cosine of 0 degrees, 360 degrees, 0pi, or 2pi will give you 1
the tan of 45 degrees, 1/4pi, 225 degrees, and 5/4 pi will all give you one