Show us what you did and we'll go from there...xdeanna said:I had some questions on a test and i got these two wrong..
x is greater than or equal to 0 and x is less than or equal to 360
1) 2sin x + sin x cos x = 0
2) sin 2x = -1/sqrt(2)
This is one solutions; there are two other numbers x in [0, 360] (deg.) for which sin(x) = 0. The inverse sine function will only produce numbers in the interval [-90, 90], in degrees. Think about where the graph of y = sin(x) crosses the x-axis.xdeanna said:2Sin x + cos x sin x = 0
Sin x(2 + cos x) = 0
sin x = 0
x= sin^-1(0)
x=0degrees
xdeanna said:or
2+ cos x= 0
cos x =-2
x= cos^-1(-2)
x=?
I did something different on the test but i think this is wrong too >.<
Don't make show what I did for #2 :(
Trig equations are mathematical equations that involve trigonometric functions such as sine, cosine, and tangent. They are used to model and solve problems related to angles and triangles.
To solve a trig equation, you need to use algebraic techniques such as factoring, the quadratic formula, or trigonometric identities. You also need to have a good understanding of the properties and graphs of trigonometric functions.
The unit circle is a circle with a radius of 1 unit that is centered at the origin (0,0) on a coordinate plane. It is used to understand the properties of trigonometric functions and their relationship to angles and triangles. Trig equations often involve angles, and the unit circle helps us visualize and solve them.
The Pythagorean identity is a trigonometric identity that states: sin²θ + cos²θ = 1. This identity is used to simplify trig equations by substituting sin²θ with 1 - cos²θ or cos²θ with 1 - sin²θ. This can help us solve equations that involve both sine and cosine functions.
Some common mistakes when solving trig equations include forgetting to check for extraneous solutions, not using the correct trigonometric identities, and making algebraic errors. It is important to always double-check your solutions and make sure they satisfy the original equation.