Find the exact value of tan 30° × sin 60°
Give your answer in its simplest form. - Edexcel - GCSE Maths - Question 16 - 2019 - Paper 1
Question 16
Find the exact value of tan 30° × sin 60°
Give your answer in its simplest form.
Worked Solution & Example Answer:Find the exact value of tan 30° × sin 60°
Give your answer in its simplest form. - Edexcel - GCSE Maths - Question 16 - 2019 - Paper 1
Step 1
Find tan 30°
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Answer
The tangent of 30 degrees is given by:
an 30° = rac{1}{ an 60°} = rac{1}{ rac{ ext{√}3}{3}} = rac{1}{3}
Step 2
Find sin 60°
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Answer
The sine of 60 degrees is:
ext{sin} 60° = rac{ ext{√}3}{2}
Step 3
Calculate tan 30° × sin 60°
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Answer
Now, substituting the values we found:
an 30° × ext{sin} 60° = rac{1}{3} × rac{ ext{√}3}{2} = rac{ ext{√}3}{6}
Step 4
Final answer
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Answer
Thus, the exact value of tan 30° × sin 60° in its simplest form is:
rac{ ext{√}3}{6}
