Objective:

To find the sine and tangents of small angles in the range 0.57° to 5.7° using the ST scale.

General:

• For small angles of θ°, the following relationship holds:

sin θ° ≈ tan θ°

We can use this approximation since

and as θ° approaches 0°, cos θ° approaches 1.  Mathematically ...

so for sufficiently small values of θ°, we can say that sin θ° ≈ tan θ°.

 

Method if the ST scale is on the Body:

• Move the cursor to the angle on the ST scale.
• Read the sine or tangent on the D scale.

Method if the ST scale is on the Slider:

• Move the cursor to the angle on the ST scale.
• Read the sine or tangent on the C scale.

 

The following examples will use the S and T scales on the Slider, a similar process is used if these scales are on the body.
Only the Slider is shown in the diagrams.

Example 1:  Calculate sin 4.36° (this is the same method to find tan 4.36°)

• Move the cursor to ST4.36
• Read the result C0.076

 

Example 2:  Calculate tan 0.75° (this is the same method to find sin 0.75°)

• Move the cursor to ST0.75
• Read the result C0.0131

 

Practice Questions:  Evaluate the following.

1. sin 0.89° (Ans: 0.0155)
2. tan 1.26° (Ans: 0.022)
3. sin 3.74° (Ans: 0.0652)
4. tan 4.8° (Ans: 0.0839)