Question

How do I found the EXACT value of the following?
1. cos (105 degrees)
2. sin (pi/12) cos (5 pi/12) + cos (pi/12) sin (5pi/12)
3. cos (2pi/3 - pi/6)
4. sin (5pi/12)

Answer 1

use sum formulas

Answer 2

cos(45+60) would work for the first one

Answer 3

I don't know what sum formulas are.

Answer 4

They should be in your trig book

Answer 5

in that section

Answer 6

http://en.wikipedia.org/wiki/List_of_trigonometric_identities#Angle_sum_and_difference_identities

Answer 7

I don't have a book!

Answer 8

:( google sum and difference identities the idea is to make addition or subtraction the number inside the () for ones like the first you are trying to make them numbers you know on the unit circle

Answer 9

Im sure if you plug those into wolfram alpha they will show you a step by step solution.

Answer 10

cos105 = cos(45+60) = cos45cos60-sin45sin60
Just put sin45 = cos45 = (sqrt2)/2 , cos60 =1/2 and sin60 =(sqrt3)/2 to the above step , you can get the exact value for it

Answer 11

Question. Why is it 45 and 60 and not 50 and 55 or some other random number?

Answer 12

because you know 45 and 60

Answer 13

Because they are the special angle for trigo function and its exact values are well-known

Answer 14

those are special angles

Answer 15

* functions and their exact values

Answer 16

Another question? Where are you getting (sqrt2)/2 , cos60 =1/2 and sin60 =(sqrt3)/2 to

Answer 17

those are the values for those special angles

Answer 18

Where can I find a list of all these values?

Answer 19

you should memorize those.

Answer 20

umm sec

Answer 21

http://www.analyzemath.com/trigonometry/special_angles.html

Answer 22

use triangles

Answer 23

eg. unit triangle 1,1,sqrt(2) has angles 45 degrees

Answer 24

I can type you one here
30 45 60
sin | 1/2 | (sqrt2)/2 | (sqrt3)/2
------------------------------------
cos | (sqrt3)/2| (sqrt2)/2 |1/2
-------------------------------------
tan | 1/sqrt3 | 1 | sqrt3

Answer 25

Sorry i'm always slow :S

Answer 26

and half an equilateral 1,sqrt(3),2 has angles 60 and 30

Answer 27

Ah I see. Let me try to get the answer and I'll tell you what I get.

Answer 28

Glad to hear!! Wait for your answer then :)

Answer 29

sin(45) = cos(45) = 1/sqrt(2)