We can solve these values using the next triangle:
First, we need to label the sides using the angle of 30 degrees.
- The largest side is always the hypotenuse, h = 1.
- The opposite side is opposite to the angle, opp = 1/2.
- The adjacent side is between the angle of 30 degrees and the right angle,
adj = √3/2.
Now, we can solve the trigonometric expressions:
For sin:
sin θ = opposite side / hypotenuse
sin 30 = (1/2) / 1
sin 30 = 1/2
For cos:
cos θ = adjacent side / hypotenuse
cos 30 = (√3/2)/1
cos 30 =√3/2
For tan:
tan θ = opposite side / adjacent side
tan 30 =(1/2) / (√3/2)
Simplify the fractions:
tan 30 = 1/√3
