Cosine and Cotangent

Objective:

To calculate cosine and cotangent of angles using the S and T scales.

General:

The trigonometrical ratios of cosine and cotangent can be found on the same S and T scales respectively.
Cosine and cotangent values are normally marked in red (on the right) increasing from right to left.
To read these scales, we make sure of the property for complementary angles (angles which add to 90°).

cos θ° = sin (90° - θ°)

cot θ° = tan (90° - θ°)

For example; cos 20° = sin 70° and cot 30° = tan 60°. This is why you see their markers at the same point on the slide rule.

These methods are assuming that the S and T scales are on the slider. If they are on the body, wherever C scale appears, use D scale.

Method to determine Cosine of an Angle:

Using the S scale and reading from right to left (generally in red), move the cursor to the angle.
Read the cosine from the C scale.

or

Use the property that cos θ° = sin (90° - θ°) and use the S scale as normal.
Read the cosine from the C scale.

Method to determine the Cotangent of an Angle:

Using the T scale and reading from right to left (generally in red), move the cursor to the angle.
Read the cotangent from the C scale.

or

Use the property that cot θ° = tan (90° - θ°) and use the T scale as normal.
Read the cotangent from the C scale.

Example 1: Calculate cos 50°.

Example 2: Calculate cot 75.4°.

Practice Questions: Evaluate the following.