Prove that sin(x)/cos(x) = tan(x)
using an angle of °
Inscribe a triangle inside a circle
The Pythagorean Theorem states
x2 + y2 = r2
The picture shows a right triangle
From the diagram, we know:
Divide sin(x) by cos(x)
Simplify the right side
Cancel r on the right side
tan(x) = (x/y)
Confirm using the angle of °
0 = 0
Final Answer
sin()/cos() = tan()
You have 2 free calculationss remaining
How does the Pythagorean Theorem Trig Proofs Calculator work?
Free Pythagorean Theorem Trig Proofs Calculator - Shows the proof of 3 pythagorean theorem related identities using the angle θ:
Sin2(θ) + Cos2(θ) = 1
Tan2(θ) + 1 = Sec2(θ)
Sin(θ)/Cos(θ) = Tan(θ)
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What 1 formula is used for the Pythagorean Theorem Trig Proofs Calculator?
sin(θ)
2 + cos(θ)
2 = 1
tan(θ)
2 + 1 = sec(θ)
2sin(θ)/cos(θ) = tan(θ)
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What 7 concepts are covered in the Pythagorean Theorem Trig Proofs Calculator?
- cosine
- cos(θ) is the ratio of the opposite side to the hypotenuse.
- proof
- an inferential argument for a mathematical statement, showing that the stated assumptions logically guarantee the conclusion
- pythagorean theorem
- a fundamental relation in Euclidean geometry among the three sides of a right triangle. It states that the area of the square whose side is the hypotenuse is equal to the sum of the areas of the squares on the other two sides
a2 + b2 = c2 - pythagorean theorem trig proofs
- sin
- sin(θ) is the ratio of the opposite side of angle θ to the hypotenuse
- tangent
- the straight line that just touches the curve at that point
- triangle
- a flat geometric figure that has three sides and three angles
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