Now, we need to find the value of cos ( π3). To do it this, let's convert first the angle of π3 to degrees. To convert π3 radians into degrees, we need to multiply by 180^(∘) and divide by π radians.
π/3 radians * 180^(∘)/π radians
Let's simplify the above expression. For simplicity, we will remove the word radians.
Then, substitute 60^(∘) for π3 in the equation.
2sin x cos (Ï€/3) ? = sin x
⇕
2sin x cos (60^(∘)) ? = sin x
Before we rewrite the given expression, let's recall the values of the three main trigonometric functions for the most important angles.
sin θ
cos θ
tan θ
θ =0^(∘)
0
1
0
θ =30^(∘)
1/2
sqrt(3)/2
sqrt(3)/3
θ =45^(∘)
sqrt(2)/2
sqrt(2)/2
1
θ =60^(∘)
sqrt(3)/2
1/2
sqrt(3)
θ =90^(∘)
1
0
-
θ =180^(∘)
0
- 1
0
θ =360^(∘)
0
1
0
Next, we will use the table above to find the exact value for the expression cos 60 ^(∘).
2sin x cos (60^(∘)) ? = sin x
⇕
2sin x (1/2) ? = sin x
Let's finally simplify the obtained expression!
