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First published on Thursday, Jan 9, 2025 and last modified on Thursday, Jan 9, 2025 by Fabienne Chaplais.
Mathedu
Angle, Trigonometry
1 Introduction
In that test, you will discover the formulae for \( \cos(2a)\) and \( \sin(3a)\) , using the trigonometric formulae you already learned.
2 Question 1: Develop \( \cos(3a)\) as \( \cos(2a+a)\)
Use the formula of the cosine of a sum to develop \( \cos(3a)\) .
3 Question 2: Develop \( \cos(3a)\) as a function of \( \cos(a)\) and \( \sin(a)\)
Use any of the formulae of the cosine and the sine of a double to develop the expression obtained in the previous section.
4 Question 3: Give \( \cos(3a)\) as a function of \( \cos(a)\)
Use the fundamental identity of the trigonometry \( \cos^2(a)+\sin^2(a)=1\) to deduce an expression of \( \cos(3a)\) that depends only on \( \cos(a)\) .
5 Question 4: Develop \( \sin(3a)\) as \( \sin(2a+a)\)
Use the formula of the sine of a sum to develop \( \sin(3a)\) .
6 Question 5: Develop \( \sin(3a)\) as a function of \( \cos(a)\) and \( \sin(a)\)
Use any of the formulae of the cosine and the sine of a double to develop the expression obtained in the previous section.
7 Question 6: Give \( \sin(3a)\) as a function of \( \sin(a)\)
Use the fundamental identity of the trigonometry \( \cos^2(a)+\sin^2(a)=1\) to deduce an expression of \( \sin(3a)\) tha depends only on \( \sin(a)\) .