Calculate sin 100° cos 55° - cos 100° sin 55°

Step by step

The question

Question: find the exact value of sin 100° cos 55° − cos 100° sin 55°.

100° and 55° 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 = 100° and B = 55°.

Careful!

The angle in the first sin is A.

So A is 100° and B is 55°.

The order matters when we take away.

So it is all one sin: sin(100° − 55°).

2 Take away the angles

100° minus 55° is 45°.

That angle is on the unit circle!

3 Use the unit circle

From the unit circle: sin 45° = √2/2.

4 Check

Let's check with the calculator.

Each one rounded: the whole thing is about 0.7071.

And √2/2 is about 0.7071.

The same!

So it is right.

Let's look back.

First: spot the rule.

Then: take away the angles.

Then: use the unit circle.

Last: check.