# exact values

• Jun 30th 2008, 04:12 PM
NoAsherelol
exact values
I am struggling today with my homework,

Find the Exact values of Tan 165 degrees ( 165 is the sum of two special angles) that is 135 degress and 30 degrees

Ok for far i have

Tan ((-Sqrt2)/2+(sqrt3)/2)=((Tan -Sqrt2/2) + (Tan sqrt3/2))/1 +(Tan -sqrt2/2)(tan Sqrt3/2)

135 is in the 2nd quadrant and tan is negative so it will be -Sqrt2/2 and 30 degrees is a 1st quadrant angle and tan is positive so its sqrt3/2

and now im stuck on this problem
• Jun 30th 2008, 04:36 PM
algebraic topology
Quote:

Originally Posted by NoAsherelol
I am struggling today with my homework,

Find the Exact values of Tan 165 degrees ( 165 is the sum of two special angles) that is 135 degress and 30 degrees

$\tan{165^{\circ}}=\tan{(135+30)^{\circ}}=\frac{\ta n{135^{\circ}}+\tan{30^{\circ}}}{1-\tan{135^{\circ}}\tan{30^{\circ}}}$

And $\tan{135^\circ}=\tan{(90+45)^\circ}=-\tan{45^\circ}$. You should be able to continue from here.
• Jun 30th 2008, 04:52 PM
mr fantastic
Quote:

Originally Posted by algebraic topology
$\tan{165^{\circ}}=\tan{(135+30)^{\circ}}=\frac{\ta n{135^{\circ}}+\tan{30^{\circ}}}{1-\tan{135^{\circ}}\tan{30^{\circ}}}$

And $\tan{135^\circ}=\tan{(90+45)^\circ}=-\tan{45^\circ}$. You should be able to continue from here.

Alternatively, tan(165) = - tan(15) = - tan(45 - 30) .....