Grade 10 · Core Mathematics · Lesson 3 of 11

Determining Trigonometric Ratios from Tables and Calculators

A Grade 10 Core Mathematics CBE lesson from the sub-strand Trigonometry 1. In it, learners read tangent values of acute angles up to two decimal places from four-figure mathematical tables using the ADD mean difference column.

Strand Measurements and GeometrySub-strand Trigonometry 1Lesson code 10CM-24-L340 minutes · 4 slides

KICD learning outcome (a)

Determine the trigonometric ratios of acute angles from mathematical tables and calculators.

By the end of this lesson, learners should be able to

Read tangent values of acute angles up to two decimal places from four-figure mathematical tables using the ADD mean difference column.
Evaluate sine, cosine, and tangent ratios of acute angles using a scientific calculator in degree mode.
Compare trigonometric table values with scientific calculator outputs to round results accurately to four decimal places.

Key vocabulary

Natural tangent: The trigonometric ratio of the opposite side to the adjacent side in a right-angled triangle.; We read the natural tangent of forty-two degrees from four-figure mathematical tables.
Mean difference: A small value in additional columns added to or subtracted from table readings.; We add a mean difference of twenty to find tangent of fifty-three point two four.
Degree mode: A calculator setting ensuring trigonometric function inputs are interpreted in angular degrees.; Set the calculator to degree mode before finding sine of fifty-four point three six.

Lesson preview

Slide 1 · Reading Tangents of Acute Angles from Four-Figure TablesOpening · 10 min

Figure 1: A section of a four-figure mathematical table showing natural tangents for angles between 10 and 13 degrees.

Four-figure mathematical tables of natural tangents allow us to determine the ratio of the opposite side to the adjacent side for any acute angle. Whole degree values are located in the main vertical column $x$ , while tenths of a degree appear across the top main columns ${0.0}^{\circ}$ to ${0.9}^{\circ}$ . For hundredths of a degree, we look under the ADD column for the required digit and add the mean difference to the last digits of the base reading. Use Figure 1 to see how tangent values are organised into columns for tenths of a degree.

Tangent tables give values for acute angles stated to two decimal places.
Whole degree angles are located in the left column x.
Tenths of a degree are read from main columns 0.0 to 0.9.
Hundredths of a degree are located in ADD columns and added to main readings.

Worked example. Locate row

42^{\circ}

down the column headed

x

. Move across row

42^{\circ}

to the main column headed

{0.3}^{\circ}

. Read the number at the intersection:

0.9099

. Answer: $\tan {42.3}^{\circ} = 0.9099$ .

Check question: What value is read from the tangent table at the intersection of row $28^{\circ}$ and main column ${0.7}^{\circ}$ ?

0.5317
0.5452
0.5475
0.5498

Show answer

0.5475. Locating row $28^{\circ}$ and moving across to column ${0.7}^{\circ}$ gives $0.5475$ .

Slide 2 · Finding Tangents with Mean DifferencesModel · 10 min

Figure 2: An excerpt from a tangent table demonstrating how to use the mean difference column to find the tangent of 37.48 degrees.

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This lesson, and every other Grade 1–10 CBE lesson, comes ready to project with the EAP ClassKit. It runs without electricity or internet.

All 4 slides with diagrams and class activities
Teacher notes, SNE adaptations and assessment checks
Homework and the other 10 lessons in this sub-strand

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Determining Trigonometric Ratios from Tables and Calculators

By the end of this lesson, learners should be able to

Key vocabulary

Lesson preview

Teach the full lesson on the projector

All 11 lessons in Trigonometry 1