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Write cosx - 3sinx in the form Rcos(x + a)

Rcos(x + a) = Rcosxcosa - Rsinxsina
By comparing cosx - 3sinx to the new expression, we can see that:
Rsina = 3 and Rcosa = 1
If we square both and add them, we can see R = √(1²+(-3)²) [I would explain why to someone I'm tutoring]
Now that we know R, we can calculate a.
a = arcsin (3/10) [you may want to adjust the value]Then just write into the form...

Answered by Odin G. • Maths tutor

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Write cosx - 3sinx in the form Rcos(x + a)

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