Math Help Forum: Exact values.

1.Find the following exact trig values:
sin210
tan300
cos270
cos(-60)
tan450
sin240

2.Name 2 angles with the value sinX=1

ASAP please!
THANKS

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!

What would be the answer to "Name 2 angles with the value sin X=1"
Also, is there a way to sketch triangles here?

Originally Posted by iluvmath101

What would be the answer to "Name 2 angles with the value sin X=1"
Also, is there a way to sketch triangles here?

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!

Originally Posted by BrendanLoftus

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!

Thanks for your help... Will it sound really stupid if I said I don't know what I'm looking at? I haven't been in math class for 2 weeks (sick) and I have a few questions I need to hand in tomorrow... Can you please just tell me what to write on my paper?

for what part?

Name 2 angles with the value sin X=1
I have a few more questions if your up to it...

Originally Posted by iluvmath101

Name 2 angles with the value sin X=1
I have a few more questions if your up to it...

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

therefore; the two angels are 90 and -270

Originally Posted by BrendanLoftus

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

thanks!