# trig

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if 5sin theta + 12cos theta is equal to 13 find the value of tan theta

• trig -

Since (5,12,13) is a Pythagorean triplet, tan(θ)=5/12.

Mathematically, we solve it by:
Divide by the right hand side:
(5/13)sin(θ)+(12/13)cos(θ)=1
Since (5/13)²+(12/13)²=1, we can put
5/13=sin(φ)
12/13=cos(φ)
so
sin(φ)sin(θ)+cos(φ)cos(&theta)=1
cos(θ-φ)=1
θ-φ=0
θ=φ=asin(5/13).

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