Determine a general formula (or formulas) for the solution to the following equa

Question

Determine a general formula (or formulas) for the solution to the following equation. Then, determine the specific solutions (if any) on the interval (0,2 pi). cos theta + sin theta = -Squareroot 2 Describe in the most concise way possible the general solution to the given equation, where k is any integer. Select the correct choice below and fill in all the answer boxes within your choice. (Simplify your answers. Type any angle measures in radians. Use the smallest non-negative angle possible when describing the genera angle possible when describing the general form of each angle. Use ascending order, entering the expression based on the smallest angle first. Type exact answers, using x as needed. Use integers or fractions for any numbers in the expressions.) theta = ___ + ___ k theta = __ + ___ k or theta = ___ + ____ k theta = ____ + ___ k or theta = ___ + ____ k or theta = ___ + ____ k theta = ____ + ____ k or theta = ___ + ____ k or theta = ____ + ____ k or theta = ____ + ____ k What are the solution(s) to the equation cos theta + sin theta = -Squareroot 2 on the interval [0, 2 pi)? Select the correct choice below and fill in any answer boxes within your choice.

Explanation / Answer

cos+sin=-2

=>(-1/2)cos+(-1/2)sin=1

=>(-1/2)cos- (1/2)sin=1

=>cos(-5/4)cos- sin(-5/4)sin=1

=>cos((-5/4)+) =1

=>((-5/4)+) =2k , k is an integer

=> =(5/4)+2k

=> =(5/4)+2k

on interval [0,2) , =(5/4)

Related Questions

Navigate

• Browse (All)
• Browse D
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.