SOLUTION: Suppose x is a real number such that 5cos(ϕ)=x where ϕ is a first quadrant angle. Find algebraic expressions (in terms of 5 and x ) for sin(ϕ) and tan(ϕ).

Question 958120: Suppose x is a real number such that 5cos(ϕ)=x where ϕ is a first quadrant angle. Find algebraic expressions (in terms of 5 and x ) for sin(ϕ) and tan(ϕ).
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
Suppose x is a real number such that 5cos(ϕ)=x where ϕ is a first quadrant angle. Find algebraic expressions (in terms of 5 and x ) for sin(ϕ) and tan(ϕ).
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5cosϕ=x
cosϕ=x/5
sinϕ=√(1-cos^2(ϕ))=√(1-x^2/25)=√((25-x^2)/25)=√(5^2-x^2)/5
tanϕ=sinϕ/cosϕ=√(5^2-x^2)/x
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SOLUTION: Suppose x is a real number such that 5cos(ϕ)=x where ϕ is a first quadrant angle. Find algebraic expressions (in terms of 5 and x ) for sin(ϕ) and tan(ϕ).