From a table of natural sines, row 25° shows 0.4226 under column 0.0 and 0.4274 under column 0.3. What is 25.3°?

Grade 10 · Core Mathematics · Lesson 1 of 11

Reading Sines and Cosines from Mathematical Tables

A Grade 10 Core Mathematics CBE lesson from the sub-strand Trigonometry 1. In it, learners locate acute angles in whole degrees and tenths using the main columns of four-figure mathematical tables.

Strand Measurements and GeometrySub-strand Trigonometry 1Lesson code 10CM-24-L140 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

Locate acute angles in whole degrees and tenths using the main columns of four-figure mathematical tables.
Apply mean differences from the ADD column to determine sine values of acute angles given to two decimal places.
Apply mean differences from the SUBTRACT column to determine cosine values of acute angles given to two decimal places.

Key vocabulary

Natural sine: The numerical ratio of the opposite side to hypotenuse for an acute angle.; We look up the natural sine of $42^{\circ}$ in four-figure mathematical tables.
Acute angle: An angle whose measure is strictly between zero degrees and ninety degrees.; The angle $42^{\circ}$ is an acute angle measured inside a right triangle.
Mean difference: A small numerical correction added or subtracted for hundredths of a degree.; The mean difference of $9$ is added to $0.6743$ giving $0.6752$ .
Trigonometric ratio: A ratio comparing the lengths of two sides in a right-angled triangle.; The sine of ${31.58}^{\circ}$ gives a trigonometric ratio equal to $0.5237$ .
Natural cosine: The numerical ratio of the adjacent side to hypotenuse for an acute angle.; Subtracting the mean difference gives the natural cosine of ${51.24}^{\circ}$ as $0.6261$ .

Lesson preview

Slide 1 · Introduction to Natural Sine TablesOpening · 10 min

Figure 1: A segment of a natural sine table highlighting the row for forty-two degrees and the columns for zero and four tenths.

Evaluating sine values for acute angles using four-figure tables or calculators is a core topic in trigonometry. A table of natural sines presents angle measures in rows alongside decimal subdivisions across columns. Finding sine values for acute angles starts by locating the whole-degree measure down the main vertical column and matching it with the desired decimal digit across the top header.

Mathematical tables assist us in finding ratio values of acute angles without making physical measurements.
To read the sine of a whole-degree angle, locate that angle in the primary column labelled $x$ .
The main columns representing tenths, from $0.0$ up to $0.9$ , supply sine values for fractional degrees.
Practising table lookup methods develops accuracy when finding sine values of acute angles in Kenya.

Worked example. Find the angle

42^{\circ}

in the first column labelled

x

. Read the value in column

0.0

, which gives

\sin 42^{\circ} = 0.6691

. Move horizontally along the same

42^{\circ}

row to column

0.4

. Read the value at the intersection, which gives

\sin {42.4}^{\circ} = 0.6743

. Answer: $\sin 42^{\circ} = 0.6691$ and $\sin {42.4}^{\circ} = 0.6743$ .

Check question: From a table of natural sines, row $25^{\circ}$ shows $0.4226$ under column $0.0$ and $0.4274$ under column $0.3$ . What is $\sin {25.3}^{\circ}$ ?

$0.4226$
$0.4229$
$0.4274$
$0.4277$

Show answer

$0.4274$ . Locating $25^{\circ}$ in column $x$ and moving across to column $0.3$ gives $0.4274$ , which is the exact value of $\sin {25.3}^{\circ}$ .

Slide 2 · Using ADD Columns for Hundredths of a DegreeModel · 10 min

Figure 2: A natural sines table demonstrating how to add the mean difference to the primary sine value for hundredths of a degree.

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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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Reading Sines and Cosines from Mathematical Tables

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