Trigonometry GCSE Maths Quiz
Test your knowledge of the Maths Topic: Trigonometry, with this quiz.
This quiz consists of 15 questions, including multiple-choice and short-answer questions on the topic of Trigonometry for GCSE Maths.
For multiple-choice questions, choose the correct answer. Scroll down to begin the quiz.
Questions
What is the value of sin(30∘)?
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Which trigonometric ratio is used to find the length of the opposite side of a right-angled triangle?
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What is the value of cos(90∘)?
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If tan(θ)=1, what is the value of θ?
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In a right-angled triangle, if the adjacent side is 6 cm and the opposite side is 8 cm, what is the length of the hypotenuse?
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In a right-angled triangle, if the opposite side is 5 cm and the hypotenuse is 13 cm, what is sin(θ)?
$sin(θ)=\frac{opposite}{hypotenuse}=\frac{5}{13}$
If cos(60∘)= ½, what is the adjacent side in a right-angled triangle where the hypotenuse is 10 cm?
Using $cos(θ) =\frac{adjacent}{hypotenuse}$
$cos(60∘)=\frac{adjacent}{10}$
$\frac{1}{2}=\frac{adjacent}{10}$
Adjacent = $10\times \frac{1}{2} = 5cm$
Find the value of tan(45∘).
tan(45∘)=1
In a right-angled triangle, if the opposite side is 7 cm and the adjacent side is 24 cm, what is the value of tan(θ)?
$tan(θ)=\frac{opposite}{adjacent} =\frac{7}{24}$
What is the length of the hypotenuse in a right-angled triangle with sides 8 cm and 15 cm, using Pythagoras' theorem?
Using the Pythagorean theorem:
$Hypotenuse^2=opposite^2+adjacent^2$
$ {Hypotenuse}^2 = 8^2 + 15^2 = 64 + 225 = 289$
${Hypotenuse} = \sqrt{289} = 17 \, \text{cm}$
Find the angle θ if sin(θ) = ⅗. (Answer in Degrees).
Using $θ = \sin^{-1} \left( \frac{3}{5} \right),$
$\theta \approx 36.87^\circ$
In a right-angled triangle, if the adjacent side is 9 cm and the hypotenuse is 15 cm, what is cos(θ)?
$cos(θ) =\frac{adjacent}{hypotenuse}=\frac{9}{15}= \frac{3}{5}$
A right-angled triangle has an opposite side of 12 cm and a hypotenuse of 13 cm. What is the value of sin(θ)?
$sin(θ) =\frac{opposite}{hypotenuse}=\frac{12}{13}$
In a right-angled triangle, if the opposite side is 9 cm and the adjacent side is 12 cm, what is tan(θ)?
$tan(θ) =\frac{opposite}{adjacent}=\frac{9}{12}=\frac{3}{4}$
If cos(θ)= ⅘ and the hypotenuse is 20 cm, what is the length of the adjacent side?
Using $cos(θ) =\frac{adjacent}{hypotenuse}$
$\frac{4}{5}=\frac{adjacent}{20}$
Adjacent $= 20\times \frac{4}{5}= 16cm$
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