Determine the values of sin θ, cos θ, tan θ, csc θ, sec θ, and cot θ at (-3, -4) on the terminal arm of an angle θ in standard position.
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hi, ill show you by doing it in a^2+b^2=c^2
Ok in order to figure out sin θ, cos θ, tan θ, csc θ, sec θ, and cot θ, you must know its properties.
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In quad 1 all of the properties are positive
In quad 2 on sin and csc are positive
In quad 3 only tan and cot are positive
In quad 4 only cos and sec are positive
For your we are in quad 3, so only tan and cot are positive.
Now one of your properties are already given.
tan θ= which is opposite over adjacent.
so tan θ= 3/4
Its positive because tan θ is positive in 3rd quad.
and since we know tanθ, we know cotθ.
cotθ is the reciprocal of tanθ, being that it is adjacent over opposite.
so cot θ = 4/3. Remember dont mark negative just because it is given that way. Follow the rules of the quads.
Now we use a^2 +b^2=c^2 formula to solve
Now Using what is above you can solve for the rest by following these rules.
sinθ= Opposite over Hypotenuse
ONLY POSITIVE IN QUAD 1 and QUAD 2
cscθ=Hypotenuse over Opposite
cosθ= Adjacent over Hypotenuse
ONLY POSITIVE IN QUAD 1 AND 4
secθ= Hypotenuse over Adjacent
HOPE YOU FOUND THIS HELPFUL! :)