Image | Equation | Discussion |
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A^{2} + B^{2} = C^{2} | This is the equation given by the Pythagorean Theorem. | |
Use the multiplicative property of equality to multiply both sides by . | ||
Since anything except zero divided by itself is one, substitute 1 for . | ||
Use the distributive property of multiplication over addition and subtraction to distribute through the parentheses on the left side of the equation. | ||
Apply the distributive property of exponentiation over division. | ||
The definition of sine is . The definition of cosine is . Given angle θ, and . Apply the substitution property of equality to substitute sin θ for and cos θ for . |
Image | Equation | Discussion |
---|---|---|
Start with the first Pythagorean identity. | ||
Apply the multiplication property of equality to the equation by multiplying both sides of the equation by . | ||
Apply the distributive property of multiplication over addition and subtraction. | ||
Since anything except zero divided by itself is one, substitute 1 for . | ||
Since 1^{2} = 1, apply the substiution property of equality to subtitute 1^{2} = 1 for 1. | ||
Apply the distributive property of exponentiation over division to both sides of the equation. | ||
Use the definition of tangent to subsitute tan θ for . | ||
Use the definition of secant to subsitute sec θ for . |
Image | Equation | Discussion |
---|---|---|
Start with the first Pythagorean identity. | ||
Apply the multiplication property of equality to the equation by multiplying both sides of the equation by . | ||
Apply the distributive property of multiplication over addition and subtraction. | ||
Since anything except zero divided by itself is one, substitute 1 for . | ||
Apply the commutative property of addition. | ||
Since 1^{2} = 1, apply the substiution property of equality to subtitute 1^{2} = 1 for 1. | ||
Apply the distributive property of exponentiation over division to both sides of the equation. | ||
Use the definition of tangent to subsitute cot θ for . | ||
Use the definition of secant to subsitute csc θ for . |
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