Trigonometry Examples

Combine tan(x)sin(x)+cos(x)
tan(x)sin(x)+cos(x)
Step 1
Given the expression asin(x)+bcos(x), find the values of k and θ.
k=a2+b2
θ=tan-1(ba)
Step 2
Calculate the value for k by substituting the coefficients from tan(x)sin(x) and cos(x) into k=a2+b2.
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Step 2.1
One to any power is one.
k=1+(1)2
Step 2.2
One to any power is one.
k=1+1
Step 2.3
Add 1 and 1.
k=2
k=2
Step 3
Find the value for θ by substituting the coefficients from tan(x)sin(x) and cos(x) into θ=tan-1(ba).
θ=tan-1(11)
Step 4
Divide 1 by 1.
tan-1(1)
Step 5
Linear combinations of trigonometric functions dictate that asin(x)+bcos(x)=ksin(x+θ). Substitute the values of k and θ.
2sin(x+π4)
 [x2  12  π  xdx ]