Determining Trigonometric Ratios Using a Calculator

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Subsection 2.4.4 Determining Trigonometric Ratios Using a Calculator

Activity 2.4.9.

\(\textbf{Work in pairs}\)

What you require:

Scientific calculators or any other calculator having \(sin\text{,}\)\(cos\) and \(tan\) battons.
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Protractor and ruler (for optional verification with a drawn triangle).
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Worksheet with a table.
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Turn on your scientific calculator.
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Ensure your calculator is set to degree mode (not radians).
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For each given angle (0°, 25°, 30°, etc.), do the following;
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- Press the sin button followed by the angle, then note the value.
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- Press the cos button followed by the angle, then note the value.
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- Press the tan button followed by the angle, then note the value.
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Record all values in the table below.

Use a calculator to find the sine, cosine, and tangent of the given angles, and fill in the table.

Angle (\(^\circ\))	\({\color{blue} sin}\)	\({\color{blue} cos}\)	\({\color{blue} tan}\)
\(0^\circ\)
\(25^\circ\)
\(30^\circ\)
\(45^\circ\)
\(60^\circ\)
\(75^\circ\)
\(90^\circ\)

Observe and Answer
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- Observe the values of sin in your table. Do they increase or decrease?
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- Compare the cosine values for different angles.
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- Why does \(tan\,90^\circ\) display a syntax error?
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Discuss your work with other learners.
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\(\textbf{Key Takeaway}\)

When given an acute angle, a calculator can be used to determine these ratios accurately.

\(\textbf{How to determine trigonometric ratios using a calculator}\text{.}\)

calculator

Ensure the calculator is in degree mode.
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- Press the "MODE" button and select "DEG" (if using a scientific calculator).
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Enter the angle value.
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- For example, to find \(sin\,30^\circ\text{,}\) type:
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  - Press sin \(\to\) Press 30 \(\to\) Press =
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  - The calculator should display \(0.5\) or some calculator will display \(\frac{1}{2}\text{.}\)
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Example 2.4.29.

Use calculator to find the following;(write your answer to \(\textbf{4 decimal places}\)).

\(sin\,40^\circ \quad cos\, 40^\circ \quad tan\,40^\circ\)

Solution.

Ensure the calculator is in degree mode

\(sin\,40^\circ\)
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Press sin \(\to\) Press 40 \(\to\) Press =
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\(sin\,40^\circ=0.6428\)
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\(cos\,40^\circ\)
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Press cos \(\to\) Press 40 \(\to\) Press =
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\(cos\,40^\circ=0.7660\)
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\(tan\,40^\circ\)
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Press tan \(\to\) Press 40 \(\to\) Press =
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\(tan\,40^\circ=0.8391\)
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Example 2.4.30.

Find \(sin\,25^\circ \quad cos\, 25^\circ \quad tan\,25^\circ\) using calculator .

Solution.

\(sin\,25^\circ\)
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Press sin \(\to\) Press 25 \(\to\) Press =
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\(sin\,25^\circ=0.4226\)
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\(cos\,25^\circ\)
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Press cos \(\to\) Press 25 \(\to\) Press =
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\(cos\,25^\circ=0.9063\)
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\(tan\,25^\circ\)
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Press tan \(\to\) Press 25 \(\to\) Press =
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\(tan\,25^\circ=0.4663\)
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\(\textbf{Exercises}\)

Use a calculator to determine the following trigonometric ratios:

Find \(sin\,35^\circ \quad cos\, 35^\circ \quad tan\,35^\circ\text{.}\)
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Find \(sin\,50^\circ \quad cos\, 50^\circ \quad tan\,50^\circ\text{.}\)
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Find \(sin\,15^\circ \quad cos\, 15^\circ \quad tan\,15^\circ\text{.}\)
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Find \(sin\,75^\circ \quad cos\, 75^\circ \quad tan\,75^\circ\text{.}\)
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