Trigonometry. Finding exact value ?

Question

How do I find the exact value of 

 

1) sin^2 30 degrees + cos^2 30 degrees

 

2) cos45degrees sin30degrees cot60degrees 

 

 

I have no idea how to solce this. It's a new topic we are learning soon in class but want to learn it at home first. In the second question do the spaces mean you multiply? Please help. 

Answer 1

Use the Unit circle for exact values of the trig ratios of 30, 45 and 60.

 

sin² 30 + cos² 30 = (1/2)² + (sqrt 3/2)² = 1/4 + 3/4 = 1  (sin² x + cos² x always equals 1

 

(cos 45)(sin 30)(cot 60) = (sqrt2/2)(1/2)(sqrt3/3) = sqrt6/12