Solving y = sec^2x - 2sin x: Tips & Strategies

[abm7]

I need to solve y = sec^2 x - 2sin x, I'm fine with the 2sin x, but for the sec^2 x...

I can't seem to understand how to do it... I can get it to...

sin^2 x + cos^2 x / cos^2 x or 1 / cos^2x

but I don't understand how to solve it when the square comes right after the cos/sin etc.

 

[Mark44]

I need to solve y = sec^2 x - 2sin x, I'm fine with the 2sin x, but for the sec^2 x...

What do you mean by "solving" this equation?
To solve an equation that involves a single variable, you isolate the variable on one side of the equation, and everything else on the other side.
When you solve an equation that involves two variables, you isolate the variable you're solving for on one side, with everything else on the other.##\sec x = \frac{1}{\cos x}##, so ##\sec^2 x = \frac{1}{\cos^2 x}##. What is ##\cos(\pi/4)##?
Your equation is already solved for y, and I don't think it's possible to solve for x in that equation.

Edit: Ah, now I understand. You want to evaluate ##\sec^2 x - 2\sin x## at ##x = \pi/4##.
This information should be in the body of the post, not just in the thread title.

I can't seem to understand how to do it... I can get it to...

sin^2 x + cos^2 x / cos^2 x or 1 / cos^2x

but I don't understand how to solve it when the square comes right after the cos/sin etc.

 

[HallsofIvy]

Now I am confused! abm7, do you want to solve [itex]y= sec^2(x)- 2sin(x)[/itex] for x, in terms of y, or do you want to evaluate it at [itex]x= \pi/4[/itex]?

"Solving" the equation will be hard- it reduces to a cubic equation for sin(x).

 

[SammyS]

I need to solve y = sec^2 x - 2sin x, I'm fine with the 2sin x, but for the sec^2 x...

I can't seem to understand how to do it... I can get it to...

sin^2 x + cos^2 x / cos^2 x or 1 / cos^2x

but I don't understand how to solve it when the square comes right after the cos/sin etc.

You need to enclose the entire numerator in parentheses as follows/

(sin^2 x + cos^2 x) / cos^2 x​

I get the sense that you don';t understand what is meant by using the exponent with the trig functions such as

sin²(x)​

All it means is to take sin(x) and square it:

sin²(x) = (sin(x))²​