# Trigonometry

posted by .

Okay, I have been given a trigonometric equation to solve (sin^2(theta) + cos(theta) = 2). So far, I have been able to use the Pythagorean identity to get (-cos^2(theta) + cos(theta) - 1 = 0), which I then multiplied by -1 on both sides to get: (cos^2(theta) - cos(theta) + 1 = 0). But, now I am stuck. I cannot figure out how to factor this equation from here. Does this equation have no solutions, or am I missing something?

• Trigonometry -

sin^2 Ø = 1 - cos^ Ø
so replace that in the original to get

1 - cos^2Ø + cosØ - 2 = 0
cos^2Ø - cosØ + 1 = 0

It does not factor , so by the quadratic formula

cosØ = (1 ± √-3)/2

since the right side is a complex number there will be no solution for Ø

## Similar Questions

1. ### Maths- complex numbers

Find tan(3 theta) in terms of tan theta Use the formula tan (a + b) = (tan a + tan b)/[1 - tan a tan b) in two steps. First, let a = b = theta and get a formula for tan (2 theta). tan (2 theta) = 2 tan theta/[(1 - tan theta)^2] Then …
2. ### Calculus

I wanted to confirm that I solved these problems correctly (we had to convert the polar curves to Cartesian equations). 1.rcos(theta)=1 x=1 2.r=2*sin(theta)+2*cos(theta) r^2=2rsin(theta)+2rcos(theta) x^2+y^2=2y+2x (a little unsure …
3. ### trigonometry

can you correct the rest for me please? Express each as a function of theta: a. sin (270deg + theta)= cos theta b. cos (pi + theta)= -cos theta c. tan (810 + theta)= ?
4. ### precalc pre ap

If theta is a rotation angle that terminates in quadrant ll and sin of theta is 5/13, find cos of theta and tan of theta. Use the first Pythagorean identity to solve for cos of theta and use quotient identity to solve for tan of theta.
5. ### math

I have a question I have been working on since yesterday and I am not making this up. I couldn't get the right answer. If sin theta = -2/3, which of the following are possible?
6. ### Precalculus

I have a precalculus test tomorrow and I've been studying nonstop for the past few days but I've been struggling because it has been 8 years since the last math class I have taken. My question is about half-angle formulas, My professor …
7. ### Trigonometry

Use a sum of difference identity to write the expression as a single function theta: cos(theta - pi). Okay so I know we will use cosAcosA+sinBsinB I got: cos(theta)cos(theta)sin(pi)sin(pi) I don't know how to solve from here and I'm …
8. ### Trigonometry

1. sin^2 theta+cos theta=2 (Hint: Use the Pythagorean identity sin^2 theta+cos theta=1 to replace sin^2 theta in the given equation.) I got no solution
9. ### Trigonometry

Prove the following identities: 1. (tan theta - sin theta)^2 + (1-cos theta)^2 = (1-sec theta) ^2 2. (1-2cos^2 theta) / sin theta cos theta = tan theta - cot theta 3. (sin theta + cos theta ) ^2 + (sin theta - cos theta ) ^2 = 2 Thank …
10. ### Trigonometry

Prove the following identities: 1. (tan theta - sin theta)^2 + (1-cos theta)^2 = (1-sec theta) ^2 2. (1-2cos^2 theta) / sin theta cos theta = tan theta - cot theta 3. (sin theta + cos theta ) ^2 + (sin theta - cos theta ) ^2 = 2 Thank …

More Similar Questions