Simplify sin(pi/3)+6cos(pi/4)

Problem

sin(π/3)+6*cos(π/4)

Solution

1. Identify the exact values for the trigonometric functions using the unit circle or special right triangles.

2. Substitute the value sin(π/3)=√(,3)/2 into the expression.

3. Substitute the value cos(π/4)=√(,2)/2 into the expression.

4. Multiply the constant 6 by the substituted value for the cosine term.

sin(π/3)+6*cos(π/4)=√(,3)/2+6*(√(,2)/2)

5. Simplify the fraction by dividing 6 by 2.

√(,3)/2+3√(,2)

6. Combine into a single fraction by finding a common denominator if required, though the simplified radical form is standard.

(√(,3)+6√(,2))/2

Final Answer

sin(π/3)+6*cos(π/4)=(√(,3)+6√(,2))/2

Want more problems? Check here!