Question 1 Easy
What is the exact value of sin 60?
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Answer: √3/2
- Opposite √3, hypotenuse 2.
- Ratio is √3/2.
- Method (1): Opposite √3, hypotenuse 2.
- Accuracy (1): Ratio is √3/2.
Exact trig values practice questions with answers
A second set of exact trig values questions for GCSE Maths. They are different from the ones on the topic page, so work through both. Try each question, then open the answer to check your working.
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Question 2 Easy
What is the exact value of cos 60?
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Answer: 1/2
- Adjacent 1, hypotenuse 2.
- Ratio is 1/2.
- Method (1): Adjacent 1, hypotenuse 2.
- Accuracy (1): Ratio is 1/2.
Question 3 Medium
What is the exact value of tan 60?
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Answer: √3
- Opposite is √3, adjacent is 1.
- Ratio is √3/1 = √3.
- Method (1): Opposite is √3, adjacent is 1.
- Accuracy (1): Ratio is √3/1 = √3.
Question 4 Medium
What is the exact value of tan 60?
Show answer
Answer: √3
- Opposite √3, adjacent 1.
- Ratio is √3/1 = √3.
- Method (1): Opposite √3, adjacent 1.
- Accuracy (1): Ratio is √3/1 = √3.
Question 5 Hard
Sin 60 equals cos of which angle?
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Answer: 30
- Complementary angles sum to 90.
- 90 - 60 = 30.
- Method (1): Complementary angles sum to 90.
- Accuracy (1): 90 - 60 = 30.
Question 6 Hard
Sin 45 equals cos of which angle?
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Answer: 45
- Complementary angles sum to 90.
- 90 - 45 = 45.
- Method (1): Complementary angles sum to 90.
- Accuracy (1): 90 - 45 = 45.
Exam-style question
A longer question with marks, in the style of a written paper. This is a Yumio practice question, not a past paper question.
Exam-style question 11 marks
Sin 20 equals cos of which angle?
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Answer: 70
- Use the cofunction identity sin θ = cos(90 - θ).
- Calculate 90 - 20 = 70.
- Mark (1): 70
Quick checks
Short one-step questions. Pick an option before you open the answer.
Check 1
What is the exact value of sin 30°?
- 1/2
- √3/2
- √2/2
Show answer
1/2 sin 30° = 1/2.
Check 2
What is the exact value of sin 45°?
- √2/2
- 1/2
- 1
Show answer
√2/2 sin 45° = 1/√2 = √2/2.
Check 3
What is the exact value of sin 60°?
- √3/2
- 1/2
- √3
Show answer
√3/2 sin 60° = √3/2.
Check 4
What is the exact value of cos 30°?
- √3/2
- 1/2
- √2/2
Show answer
√3/2 cos 30° = sin 60° = √3/2.
Check 5
What is the exact value of cos 60°?
- 1/2
- √3/2
- 0
Show answer
1/2 cos 60° = sin 30° = 1/2.
Check 6
What is the exact value of cos 45°?
- √2/2
- 1/2
- √3/2
Show answer
√2/2 cos 45° = sin 45° = √2/2.
Check 7
What is the exact value of tan 45°?
- 1
- √3
- √3/3
Show answer
1 tan 45° = 1/1 = 1.
Check 8
What is the exact value of tan 60°?
- √3
- √3/3
- 1
Show answer
√3 tan 60° = √3 / 1 = √3.
Check 9
What is the exact value of tan 30°?
- √3/3
- √3
- 1/2
Show answer
√3/3 tan 30° = 1/√3 = √3/3.
Check 10
sin 30° is equal to the cosine of which angle?
- 60°
- 30°
- 45°
Show answer
60° Complementary angles: sin θ = cos(90° - θ).
Check 11
sin 60° is equal to the cosine of which angle?
- 30°
- 60°
- 45°
Show answer
30° 90° - 60° = 30°.
Check 12
sin 45° is equal to the cosine of which angle?
- 45°
- 90°
- 0°
Show answer
45° 90° - 45° = 45°.
Check 13
Why must exact trig values not be written as decimals?
- Decimals are rounded approximations of irrational surds
- Calculators cannot do trig
- Exams only test fractions
Show answer
Decimals are rounded approximations of irrational surds Surds like √3/2 are irrational and decimals lose exact precision.
Check 14
What is 1/√3 when its denominator is rationalised?
- √3/3
- 3/√3
- 1/3
Show answer
√3/3 Multiply numerator and denominator by √3: (1×√3)/(√3×√3) = √3/3.
Check 15
Which trig ratio is always 1 for 45°?
- tan 45°
- sin 45°
- cos 45°
Show answer
tan 45° In an isosceles right triangle, opposite = adjacent so tan = 1.
Keep going with Exact trig values
Practise free
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