Posted by **Anonymous** on Saturday, June 15, 2013 at 8:41am.

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

- trig -
**MathMate**, Saturday, June 15, 2013 at 11:03am
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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