-2
votes
1answer
24 views

Help on Quadratic Equations [on hold]

If $\sin15$ and $\cos 15$ are the roots of a quadratic equation $x^2+ax+b=0$, then find the value of $a^4- b^2$. Please, need help, show working, thanks.
3
votes
1answer
29 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
61 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
115 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
57 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
226 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 ...