Evaluate: cos60 - sin270 + sin330 + cos90. (Do not use a calculator.)?

Question

I don't need the answer (it would be nice), just how to solve the problem.

Answer 1

So there are a few things to remember for certain triangles:

30-60-90 triangles have legs lengths opposite the angles of: 1, sqrt(3), 2 respectively (where 2 is the hypotenuse since it is opposite the 90).

With that being said, let's dive right in.

Cosine of 60 would be adjacent over hypotenuse. The opposite leg of 60 is sqrt(3), so that leaves the 1 to be the adjacent leg.

This gives:
cos(60)=1/2

Sin 270 is basically 90 the other way on the unit circle (which you should really read up on, it's saved my butt countless times). That is -1.

Sin 330 is 30 the other way on the unit circle. Sin(-30) gives you
-1/2 from what I said earlier.

Finally cos (90) is zero due to unit circle.

All in all you get:

1/2-(-1)-1/2+0

Which is:
1



Link to unit circle:
http://www.mathematicshelpcentral.com/lecture_notes/precalculus_trigonometry_folder/unit_circle.htm

Answer 2

There are some things that it just makes sense to memorize.

sin(0) = cos(90) = cos(π/2) = (1/2) √0
sin(30) = sin(π/6) = cos(60) = cos(π/3) = (1/2) √1
sin(45) = sin(π/4) = cos(45) = cos(π/4) = (1/2) √2
sin(60) = sin(π/3) = cos(30) = cos(π/6) = (1/2) √3
sin(90) = sin(π/2) = cos(0) = (1/2) √4

That way the beauty of the symmetry really shines through.

And, as someone else said, get tight with the unit circle. It'll save you on a lot of occassions (just ask me how I know )


Doug

Answer 3

cos = 1 at 0, 0 at 90, -1 at 180, 0 at 270, and 1 at 360
sin = 0 at 0, 1 at 90, 0 at 180, -1 at 270, and 0 at 360

cos 60 = 1/2
sin 270 = -1
sin 330 = -1/2
cos 90 = 0

1/2 - (-1) + (-1/2) + 0 = 1/2 + 1 - 1/2 = 1

Answer 4

= cos60 - sin(360 - 270) + sin(360 - 330) + cos90
= cos60 - ( - sin90) + ( - sin30) + cos90
= cos60 + sin90 - sin30 + cos90
= 1/2 + 1 - 1/2 + 0
=1

There you go..... : )

Answer 5

cos 60*-sin(180*+90*)+sin(360*-30*)+cos 90*
=cos 60*+sin 90*+sin -30*+cos 90*
=1/2+1-1/2+0=1

Answer 6

cos(60) - sin(270) + sin(330) + cos(90)
cos(60) - sin(-90) + sin(330) + cos(90)
cos(60) + sin(90) + sin(330) + cos(90)
cos(60) + cos(90) + sin(90) + sin(330)
cos(60) + 0 + 1 + sin(-30)
cos(60) + 1 - sin(30)
(1/2) + 1 - (1/2)
1

ANS : 1

Answer 7

answer is 1 .Refer your high school trigonometry book