Find the exact value of each of the following. Please explain how you got the answer.

sin 17pi /6 =

tan 13pi/4 =

sec 11pi/3 =

Guest Feb 3, 2019

#1**+2 **

First, let's figure out what the following things are in degrees.

17pi/ 6 radians is 510 degrees. By the periodicity identity, we need to find sin 510-360 = 150.

Think about it in the unit circle. Then, you will find that sin 150 = sin 30, which is just **1/2.**

13 pi / 4 radians is 585 degrees. By periodicity identity, 585-180-180-180 = 45. tan = sin/cos, and since sin and cos are the same at 45 degrees, then tan 45 = **1.**

11pi/3 radians is 660 degrees. By periodicity, 660-360 = 300. sec = 1/cos, and so if we think about in the unit circle, we have cos 300 = cos 60. cos 60, obviously is just **sqrt3 /2. **

If you don't understand why sin 30 is 1/2 and cos 60 is sqrt3/2, then think of special right triangles.

itsyaboi Feb 3, 2019

#1**+2 **

Best Answer

First, let's figure out what the following things are in degrees.

17pi/ 6 radians is 510 degrees. By the periodicity identity, we need to find sin 510-360 = 150.

Think about it in the unit circle. Then, you will find that sin 150 = sin 30, which is just **1/2.**

13 pi / 4 radians is 585 degrees. By periodicity identity, 585-180-180-180 = 45. tan = sin/cos, and since sin and cos are the same at 45 degrees, then tan 45 = **1.**

11pi/3 radians is 660 degrees. By periodicity, 660-360 = 300. sec = 1/cos, and so if we think about in the unit circle, we have cos 300 = cos 60. cos 60, obviously is just **sqrt3 /2. **

If you don't understand why sin 30 is 1/2 and cos 60 is sqrt3/2, then think of special right triangles.

itsyaboi Feb 3, 2019