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Question
Find the value of sin−1(cos33π5)
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Solution
We need to find the value of sin−1(cos(33π5))
sin−1(cos(33π5))=sin−1(cos(30π+3π5))
=sin−1(cos(6π+3π5))
=sin−1(cos(3π5))
=sin−1(sin(π2−3π5))
=sin−1(sin(−π10))
=−π10{∵sin−1(sinx)=x,forx∈[−π2,π2]}
∴sin−1(cos(33π5))=−π10
We need to find the value of sin−1(cos(33π5))
sin−1(cos(33π5))=sin−1(cos(30π+3π5))
=sin−1(cos(6π+3π5))
=sin−1(cos(3π5))
=sin−1(sin(π2−3π5))
=sin−1(sin(−π10))
=−π10{∵sin−1(sinx)=x,forx∈[−π2,π2]}
∴sin−1(cos(33π5))=−π10
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