1. ## Trig Help

I am having trouble finding the period, and amp from ↓ and simplifying

1. Whats the period of the graph of y = 2cos^2 5X -1

period = 2pie/b. I cannot define what the b is. In theory it should be 5, but the power has taken its effect.

2. For y= 5sinXcosX +1, find its amplitude,period, and its range, and its X intercepts X = all real numbers

no idea how to start.^^;

3. simplify sin^2 X + sec^2 X + tan^2 X + cos^2 X
a.2
b. 1+sin^2X/cos^2X
c.2sec^2X
d.2tan^2X

here is what i have done, first finding the common denominator.

= sin^2 X + 1 + Sin^2X + cos^2X
/ cos^2X cos^2X

= (sin^2X)(Cos^2X)+1+Sin^2X+(cos^2X)(cos^2X)
/ cos^2X

then i got stuck..

$\displaystyle \cos^2(x)=\frac{1+\cos(2x)}{2}$

Use that to get the expression in a better form.

3. Originally Posted by hovermet
I am having trouble finding the period, and amp from ↓ and simplifying

1. Whats the period of the graph of y = 2cos^2 5X -1

period = 2pie/b. I cannot define what the b is. In theory it should be 5, but the power has taken its effect.

2. For y= 5sinXcosX +1, find its amplitude,period, and its range, and its X intercepts X = all real numbers

no idea how to start.^^;

3. simplify sin^2 X + sec^2 X + tan^2 X + cos^2 X
a.2
b. 1+sin^2X/cos^2X
c.2sec^2X
d.2tan^2X

here is what i have done, first finding the common denominator.

= sin^2 X + 1 + Sin^2X + cos^2X
/ cos^2X cos^2X

= (sin^2X)(Cos^2X)+1+Sin^2X+(cos^2X)(cos^2X)
/ cos^2X

then i got stuck..
2. $\displaystyle y = 5\sin{x}\cos{x} + 1$

Use the double angle identity for sine:

$\displaystyle \sin{2\theta} = 2\sin{\theta}\cos{\theta}$.

$\displaystyle y = 5\sin{x}\cos{x} + 1$

$\displaystyle = \frac{5}{2}\cdot 2\sin{x}\cos{x} + 1$

$\displaystyle = \frac{5}{2}\sin{2x} + 1$

You should be able to go from here...