How to find the exact value of the sin, cos, and tan of the angle -105 degrees?

Seamus Livingston

Seamus Livingston

Answered question

2023-02-02

How to find the exact value of the sin, cos, and tan of the angle -105 degrees?

Answer & Explanation

anacapicuai1i

anacapicuai1i

Beginner2023-02-03Added 7 answers

Given solution: sin ( - 105 )
= sin ( - 60 - 45 )
= sin ( ( - 60 ) + ( - 45 ) )
= sin ( - 60 ) cos ( - 45 ) + cos ( - 60 ) sin ( - 45 )
= - 3 2 × 2 2 + 1 2 × - 2 2
= - 6 4 - 2 4
= - 6 - 2 4
cos ( - 105 )
= cos ( - 60 - 45 )
= cos ( ( - 60 ) + ( - 45 ) )
= cos ( - 60 ) cos ( - 45 ) - sin ( - 60 ) sin ( - 45 )
= 1 2 × 2 2 - ( - 3 2 × - 2 2 )
= 2 4 - 6 4
= 2 - 6 4
tan ( - 105 )
= tan ( ( - 60 ) + ( - 45 ) )
= tan ( ( - 60 ) + ( - 45 ) )
= tan ( - 60 ) + tan ( - 45 ) 1 - tan ( - 60 ) tan ( - 45 )
= - 3 - 1 1 - ( - 3 ) ( - 1 )
= - 3 - 1 1 - 3
= - ( 3 + 1 ) 1 - 3
= 3 + 1 3 - 1

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