Trignometry equations

Question

Solve 4 sin x + 5 = 4 sin x to the nearest thousandth over for

1.the domain 0°<=x <360°

2.the real numbers

 

 

Solve sec2 θ=sec θ + 2 using exact values over

1.the domain -2pi≤ x  <2pi

2. real numbers

Answer 1

Youve asked to solve:  4 sin x + 5 = 4 sin x.

 

This equation implies that 5 = 0; no solution.

 

 

You also ask to Solve sec² θ=sec θ + 2, which is equivalent to u² - u - 2 = 0 if we temporarily let u = sec θ.

 

solve that by factoring, then take that answer and set it to 1/cos θ, which is the secant.

 

Reject any u-solution whose absolute value is less than 1, since u represents the secant.