As we know, there are an infinite number of answers. We will find the first 2 positive angles whose cosine is `0.7`.

From our calculator, we have one answer: cos^{-1}0.7 = 45.57°.

Since this is an acute angle, we can use it as the **reference** angle and write *α* = 45.57°.

To find another answer, we remember that the 2 places where
**cosine** is positive are the first (I) and fourth (IV)
quadrants. The corresponding angle in the fourth quadrant will
be:

360° −

α= 360° − 45.57° = 314.43°

**Check:** cos 45.57° = 0.7000373 and

cos 314.43° = 0.7000373

Of course, there are an infinite number of angles where the cosine of the angle is `0.7`. Here are some of them (the values where the red arrows are pointing):

Try the values in your calculator (eg cos 1125.6°) to convince yourself that they are correct. (Your answer rounded to one decimal place should be `0.7` for each one.)

Checking your answers helps you to understand what is going on and it is great for building confidence in mathematics!