Question

Without using a calculator, evaluate
(cos(30))^2−(sin(30))^2=

30's are degrees.

Answer 1

use the identity :
cos^2 (x) - sin^2 (x) = cos(2x)

Answer 2

here,given x=30 deg

Answer 3

oh and the 2's are supposed to be like ^2. not just multiplying.

Answer 4

yup, that is a squared sign

Answer 5

yes i know... i was just letting you know. so what you said is still right, correct?

Answer 6

if u put x=30 to the identity above :
cos^2 (x) - sin^2 (x) = cos(2x), giving us
cos^2 (30) - sin^2 (30) = cos(2 * 30) = cos60, right ?

Answer 7

i dont get where you are getting cos(2x)...

Answer 8

that is one of identity in trigono, it must be in ur book, right

Answer 9

uhm, i am sure it is. but we didnt learn it that way. anyway, continue.

Answer 10

well, the alternative way
did u memorize the value of sine, cos, tangen for the specials angles in trigo ?

Answer 11

cos30 and sin30 is very familiar, because it is the special angle

Answer 12

whatt's
cos30 = ...
sin30 = ...

Answer 13

i have the unit circle? if that is what you mean...

Answer 14

sqrt3/2 correct?

Answer 15

and 1/2

Answer 16

yup, for cos30

Answer 17

correct again :)

Answer 18

yayyyyy (:

Answer 19

so sqrt3/2-1/2...

Answer 20

now, the original ques is
cos30 squared - sin30 squared
= (sqrt(3)/2)^2 - (1/2)^2
= 3/4 - 1/4
= ... ?

Answer 21

1/2 :D

Answer 22

you are my new friend!!! thank you sooooo mush :DDD

Answer 23

that's right
it's same like cos60, what i said before :)

Answer 24

you're welcome

Answer 25

wow thats an easier way of thinking about it!

Answer 26

actually, YES!! hhe

Answer 27

this woman has us going around the world when we can just walk across the street -_-