Calculate sin 50° cos 10° + cos 50° sin 10°

Step by step

The question

Question: find the exact value of sin 50° cos 10° + cos 50° sin 10°.

50° and 10° are not on the unit circle.

1 Spot the rule

This is the right side of a rule we know: sin(A + B) = sin A cos B + cos A sin B.

With A = 50° and B = 10°.

Careful!

The angle in the first sin is A.

So A is 50° and B is 10°.

The order matters when we take away.

So it is all one sin: sin(50° + 10°).

2 Add the angles

50° plus 10° is 60°.

That angle is on the unit circle!

3 Use the unit circle

From the unit circle: sin 60° = √3/2.

4 Check

Let's check with the calculator.

Each one rounded: the whole thing is about 0.8660.

And √3/2 is about 0.8660.

The same!

So it is right.

Let's look back.

First: spot the rule.

Then: add the angles.

Then: use the unit circle.

Last: check.