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# trig

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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 =

Feb 3, 2019

#1
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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.

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