Question

Algebra II: Special values practice (NO CALCULATOR)

1) tan 240
2) csc pi
3) sin pi/4

Answer 1

Hints:

\[\Large \tan(\theta) = \frac{\sin(\theta)}{\cos(\theta)}\]

\[\Large \tan(2*\theta) = \frac{\sin(2*\theta)}{\cos(2*\theta)}\]

\[\Large \tan(2*120) = \frac{\sin(2*120)}{\cos(2*120)}\]

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\[\Large \sin(2\theta) = 2\sin(\theta)\cos(\theta)\]


\[\Large \cos(2\theta) = 2\cos^2(\theta)-1\]


http://tutorial.math.lamar.edu/pdf/Trig_Cheat_Sheet.pdf

Answer 2

let me know if that helps

Answer 3

not really

Answer 4

are you able to use the unit circle to determine what sin(120) is equal to?

Answer 5

yes

Answer 6

what is sin(120) equal to?

Answer 7

https://upload.wikimedia.org/wikipedia/commons/thumb/4/4c/Unit_circle_angles_color.svg/2000px-Unit_circle_angles_color.svg.png


Locate the angle 120 degrees
the y coordinate of the point on the unit circle will be equal to `sin(120)`

Answer 8

where are you getting 120 from?

Answer 9

oh wait, I'm not thinking. I was all set to use the double angle formula when 240 is already on the unit circle

nevermind

Answer 10

Locate the angle 240 degrees
the y coordinate of the point on the unit circle will be equal to sin(240)

Answer 11

how do I know what angle 240 is?

Answer 12

>:( why doesn't my teacher teach me?

Answer 13

see attached

Answer 14

I circled the angle 240 degrees

the corresponding point to 240 degrees is \[\Large \left(-\frac{1}{2}, -\frac{\sqrt{3}}{2}\right)\]

Answer 15

hopefully you're seeing what I'm referring to?

Answer 16

I don't understand how to get to the coordinates

Answer 17

the coordinates are shown on the image as a reference to look up

if you cannot use the unit circle for a test or something like that, then there's another way to find the coordinates

first you need the reference angle

240 - 180 = 60 degrees

Answer 18

the hypotenuse is always 1 unit (unit circle ---> radius 1 unit ---> hypotenuse 1 unit)

Answer 19

the side opposite the 30 degree angle is half as long as the hypotenuse

Answer 20

and the side opposite the 60 degrees is equal to the short leg times sqrt(3)