Geometry: An Interactive Journey to Mastery

Lesson 18: What Is the Sine of 1°?

Example 1

A calculator gives sin 1° |0.017. What, then, is sin 2° and sin 3°?

Solution

7KHREYLRXVDQVZHULVWRXVHDFDOFXODWRUDJDLQWRFRPSXWHWKHVHYDOXHV+RZHYHUZLWKRXWLWZHFDQGRWKH

following.

sin 2° 2 sin 1° cos 1°.

Next, cos 1^22  sin 1 1 shows that cos 1  |1 sin 1^22 1 0.017 , so

sin 2° |uu|2 sin 1° cos 1° 2 0.017 1 0.017^2 0.034.

Also,

(^22)
sin 3° sin 1° 2°
sin 1 cos 2 cos 1 sin 2
0.017 1 0.034 1 0.017 0.034
0.051.





|u  u

|

Example 2

Find all three angles of the triangle in Figure 18.1.

Solution

We have 5222  10 11 220 cos ,z giving cos z 196220.

8VLQJWKH³cos^1 ” button on a calculator to convert the answer to a cosine value and return the original angle,

we see the following.

z |cos^1 §· ̈ ̧©¹^196220 27.0°.

Also, 11 22 2   5 10 100 cos ,x giving x |cos^11004 87.7°, and 10 22 2   5 11 110 cos ,y

giving y |cos^111046 65.3°.

Study Tip

x There is no need to memorize the formulas in this lesson. Just look them up if ever you need them.

x

y

10 z

(^511)
Figure 18.1