0
votes
5answers
54 views

Solving a quadratic trigonometric equation?

The equation is $6 \cos^2x+\cos x=1$, My work: $6x^2+x-1=0$ $(3x-1)(2x+1)$ $3x-1=0 ∨ 2x+1=0$ $x=\frac{1}{3} ∨ x= \frac{-1}{2}$ But I do not know how to progress further.
0
votes
1answer
77 views

Find pressure in a sinusoidal function

Tiffany is a model rocket enthusiast. She has been working on a pressurized rocket filled with laughing gas. According to her design, if the atmospheric pressure exerted on the rocket is less than 10 ...
3
votes
1answer
30 views

Finding number of solutions.

How many solutions does this equation have $$2 \cos^2\left(\frac12 x \right) \sin^2 x = x^2+x-2$$ where $0 \lt x \le \displaystyle\frac \pi9?$ I observed that $2 \cos^2\left(\frac12x\right)$ can be ...
-1
votes
2answers
66 views

I need help with a trig proof. [duplicate]

without a calculator, prove $\sin^2 x- 6\sin x-5=0$ has more than one real solution. I have repeatedly solved this but I have only got one solution. Can someone help me out! Show your work how you ...
3
votes
2answers
129 views

For what $x\in[0,2\pi]$ is $\sin x < \cos 2x$

What's the set of all solutions to the inequality $\sin x < \cos 2x$ for $x \in [0, 2\pi]$? I know the answer is $[0, \frac{\pi}{6}) \cup (\frac{5\pi}{6}, \frac{3\pi}{2}) \cup (\frac{3\pi}{2}, ...
3
votes
1answer
66 views

Scale change on Quadratic

Consider the two functions $f(x)=ax^2$ and $g(x)=bx^2$. Using this transformation form $T(x,y)=(cx,cy)$, find a scale change that maps $f(x)$ onto $g(x)$
1
vote
2answers
264 views

Solving a quadratic equation via a tangent half-angle formula

(Maybe I'll post my own answer here, but maybe others will make that redundant.) This is a fun (?) trivia item that fell out of a bit of geometry I was thinking about. One of the tangent half-angle ...