find the algebraic expression that is equal to sin (-theta) sec(-theta) cot(-theta)
sin(-θ) = -sinθ
sec(-θ) = secθ
cot(-θ) = -cotθ
So, you have
(-sinθ)(secθ)(-cotθ) = 1
Well, well, well! Looks like you've got yourself a real math mystery here. Let's solve it with a touch of clownish algebraic humor, shall we?
First, let's break it down step by step:
sin(-θ) is equal to -sin(θ) when θ is in degrees. So, we can rewrite it as -sin(θ).
Next, since sec(-θ) is equal to 1/cos(-θ), which simplifies to 1/cos(θ), we can rewrite it as sec(-θ) = sec(θ) = 1/cos(θ).
Finally, cot(-θ) is equal to 1/tan(-θ), which can be rewritten as 1/(-tan(θ)) or -1/tan(θ).
Now, let's put it all together:
Expression = sin(-θ) * sec(-θ) * cot(-θ)
= (-sin(θ)) * (1/cos(θ)) * (-1/tan(θ))
= sin(θ) / (cos(θ) * tan(θ))
Voilà! The algebraic expression equivalent to sin(-θ) * sec(-θ) * cot(-θ) is sin(θ) / (cos(θ) * tan(θ)). Happy solving!
To simplify and find the algebraic expression that is equal to sin(-θ)sec(-θ)cot(-θ), we can start by using trigonometric identities.
1. Recall that sin(-θ) is equal to -sin(θ) and cot(-θ) is equal to -cot(θ).
2. Substituting these values, the expression becomes -sin(θ)sec(-θ)(-cot(θ)).
3. Next, we know that sec(θ) is equal to 1/cos(θ). Replacing sec(-θ) with 1/cos(-θ), the expression becomes -sin(θ)(1/cos(-θ))(-cot(θ)).
4. Now, cos(-θ) is equal to cos(θ), so we can simplify the expression to -sin(θ)(1/cos(θ))(-cot(θ)).
5. Lastly, the product of sin(θ) and cot(θ) is equal to cos(θ). Therefore, the expression can be written as -sin(θ)(1/cos(θ))(-cot(θ)) = -sin(θ)(1/cos(θ))(-cos(θ)).
After simplifying, the algebraic expression that is equal to sin(-θ)sec(-θ)cot(-θ) is -sin(θ)(1/cos(θ))(-cos(θ)).
To find the algebraic expression that is equal to sin(-theta) sec(-theta) cot(-theta), we'll break it down step by step.
First, let's recall the trigonometric identities for sine, secant, and cotangent:
1. sin(-theta) = -sin(theta) (odd function)
2. sec(-theta) = sec(theta) (even function)
3. cot(-theta) = -cot(theta) (odd function)
Now, substituting these identities into the given expression, we get:
-sin(theta) * sec(theta) * (-cot(theta))
Next, simplify the expression:
-sin(theta) * sec(theta) * (-cot(theta)) = sin(theta) * sec(theta) * cot(theta)
Therefore, the algebraic expression that is equal to sin(-theta) sec(-theta) cot(-theta) is sin(theta) * sec(theta) * cot(theta).