Grade 10 · CAPS

Grade 10 Trigonometry

Maths practice questions and a worked example

Grade 10 Trigonometry covers defining and applying the trigonometric ratios in right-angled triangles, solving trigonometric equations, simplifying expressions using reduction formulae and identities, sketching sine/cosine graphs, and applying trigonometry to angle-of-elevation problems. Drawn from real November 2022-2023 Paper 2 content, including the classic 'two ladders against a wall' and 'angle of elevation to two windows' style application questions.

Worked example

4.1.1 If

x = 66, 4^{\circ}

and

y = 114, 7^{\circ}

, evaluate the following correct to TWO decimal places:

cos (x + y)

Answer & explanation

-1

To evaluate \

\cos(x + y)\

where \

x = 66.4^\circ\

and \

y = 114.7^\circ\

, first find \

x + y\

: 1. Calculate \

x + y = 66.4^\circ + 114.7^\circ = 181.1^\circ\

. 2. Use the cosine function: \

\cos(181.1^\circ)\

. 3. Since \

181.1^\circ\

is just over \

180^\circ\

, \

\cos(181.1^\circ)\

is very close to \

-1\

. 4. Calculate \

\cos(181.1^\circ)\

using a calculator to get approximately \

-0.9998477\

. 5. Round this to two decimal places: \

-1.00\

. Thus, \

\cos(x + y)\

correct to two decimal places is \

-1.00\

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Trigonometry

Question 1 of 3

4.1.2 If

x = 66, 4^{\circ}

and

y = 114, 7^{\circ}

, evaluate the following correct to TWO decimal places:

2 sin x

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Common mistakes

Forgetting to check the given quadrant/range before choosing the reference angle sign, and mixing up cosec/sec/cot with their reciprocal ratios.

Grade 10 Trigonometry

Worked example

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