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allisonhe
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.
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.
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. |dw:1366290912052:dw|
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! :)
Did you find the rest?
yes, and i think this helpful
Ok Happy to know! Have a great Day!