please help me solve these trignometric problems?

Question

I can't type the symbols for degrees here so please excuse me for that. The terms in degrees are in the brackets.

1. sin ^ 2( 30) - 2 cos ^ 3 (60) + 3 tan ^ 4 (45)
2. {cos ( 0 ) + sin (45) + sin (30 ) } { sin (90) - cos (45) + cos (60) }

I'm getting the answers as 1) . 3 and 2) 1 3/4 , but I 'm not sure.

Answer 1

yes you are absolutely correct.
I'l show you the working here:

1) . sin ^ 2( 30) - 2 cos ^ 3 (60) + 3 tan ^ 4 (45)

sin 30 = 1/2 , cos 60 = 1/2 , tan 45 = 1

so,

substituting the values
(1/2) ^ 2 - 2 (1/2) ^ 3 + 3(1) ^ 4
1/4 - 2 * 1/8 + 3*1
1/4 - 1/4 + 3 = 3

2) . {cos ( 0 ) + sin (45) + sin (30 ) } { sin (90) - cos (45) + cos (60) }

cos 0 = 1, sin 45 = 1/sqrt 2 , sin 30 = 1/2, sin 90 = 1, cos 45 = 1/ sqrt 2 , cos 60 = 1/2

substituting these values

(1 + 1/sqrt 2 + 1/2 ) ( 1 - 1/ sqrt 2 + 1/2)
(3/2 + 1/sqrt 2 ) ( 3/2 - 1/ sqrt 2)
(3/2) ^ 2 - ( 1/ sqrt 2) ^ 2
9/4 - 1/2
(9 -2) / 4
7/4
1 3/4

Answer 2

I don't want to help you cheat, but if you think you're getting the wrong answers, make sure your calculator is in degree mode, and not radian.

Answer 3

I get the same answers:
1.) 3
2.) 1.75

Answer 4

yup u r definately right
gud luck