# Need help with another AL Maths Question

https://www.quora.com/profile/Bravewarrior/Need-help-with-part-a-of-this-question-1
Here is the question and solution. I'm confused as to how in part a they suddenly got 3sin theta. Any help would be appreciated!
Original post by pigeonwarrior
https://www.quora.com/profile/Bravewarrior/Need-help-with-part-a-of-this-question-1
Here is the question and solution. I'm confused as to how in part a they suddenly got 3sin theta. Any help would be appreciated!

By definition, cos is the COmplementary angle SIN so
cos(x) = sin(pi/2 - x)
or
cos(pi/2 - x) = sin(x)
Its one of the basic identities which drops out of a simple right triangle, which has two complementary angles.
Original post by mqb2766
By definition, cos is the COmplementary angle SIN so
cos(x) = sin(pi/2 - x)
or
cos(pi/2 - x) = sin(x)
Its one of the basic identities which drops out of a simple right triangle, which has two complementary angles.

Ohhh so as the cosine graph is just a shifted version of the sine graph, for this question we assume that cos(pi/2-x) is the same as sine? As it is so similar to the sine graph?
Original post by pigeonwarrior
Ohhh so as the cosine graph is just a shifted version of the sine graph, for this question we assume that cos(pi/2-x) is the same as sine? As it is so similar to the sine graph?

The previous (two) identity is how cos is defined. So if you have
A+B=90
Then
cos(A)=sin(B)
and sin(A)=cos(B) and they should be clear if you sketch a right triangle and think about which side ratios they refer to. So as you say the cos and sin curves are identical apart from a shift by pi/2.

Edit - if you didbt spot it, you could expand cos(pi/2-theta) using the usual angle addition identity and get the above the long way.
(edited 2 months ago)
Original post by mqb2766
The previous (two) identity is how cos is defined. So if you have
A+B=90
Then
cos(A)=sin(B)
and sin(A)=cos(B) and they should be clear if you sketch a right triangle and think about which side ratios they refer to. So as you say the cos and sin curves are identical apart from a shift by pi/2.

Edit - if you didbt spot it, you could expand cos(pi/2-theta) using the usual angle addition identity and get the above the long way.

Ohhh ok thank you so so much!!!