Trigonometric Functionssimplify sin squared functions

In summary, the conversation is discussing how to simplify the equation 2sin^2x-3sinx-2=0 to (2sinx+1)(sinx-2)=0 using substitution and factoring. The speaker also mentions that if one is not allowed to use this method, they may need to use trig identities to solve the equation.
  • #1
ku1005
66
0
just looking at another question to do with trigonometric functions and I can't see how they simplify the follwing:
2sin^2x-3sinx-2=0 to
(2sinx+1)(sinx-2)=0
again i prob thinking sumthin really stupid...but i can't see wat! cheers
 
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  • #2
The equation can be treated like a normal quadratic equation.

use substitution and replace "sinx" with "x"
2(sinx)^2-3sinx-2=0 ----> 2x^2-3x-2=0

factor the equation
2x^2-3x-2=0 = (2x+1)(x-2)

Replace "x" with "sinx"
(2x+1)(x-2)=0 -----> (2sinx+1)(sinx-2)=0


If you aren't allowed to use this method and you have to use trig identities then someone else will have to help. I'm too lazy to look up or derive the identities right now :-p
 
  • #3
cheers mate...and i like ur thinkin! LOL
 

1. What are the basic trigonometric functions?

The basic trigonometric functions are sine, cosine, and tangent. These functions represent the ratios of the sides of a right triangle.

2. How do I simplify a trigonometric function with squared terms?

To simplify a trigonometric function with squared terms, you can use the Pythagorean identity, which states that sin²(x) + cos²(x) = 1. This identity allows you to rewrite squared functions in terms of the other trigonometric functions.

3. Can I use a calculator to simplify trigonometric functions?

Yes, most scientific calculators have buttons for sine, cosine, and tangent, making it easy to simplify these functions. However, it is important to know how to simplify them by hand as well.

4. How do I solve a trigonometric equation with multiple squared terms?

To solve a trigonometric equation with multiple squared terms, you can use the Pythagorean identity to rewrite the equation in terms of one trigonometric function. Then, use algebraic methods to solve for the unknown variable.

5. What is the difference between sin²(x) and (sin(x))²?

There is no difference between sin²(x) and (sin(x))². Both notations represent the squared of the sine function, and they can be used interchangeably.

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