Case Name |
Step 1 - Exponent Manipulation |
Step 2 |
Step 3 |
Step 4 |
Sine-Odd and Cosine-Even |
Manipulate sine powers to Manipulate to sin(x)(sin2(x))p |
Sine Pythagorean Id. |
Let u=cos(x) |
Sine-Even and Cosine-Odd |
Manipulate sine powers to Manipulate to cos(x)(cos2(x))p |
Cosine Pythagorean Id. |
Let u=sin(x) |
Sine-Odd and Cosine-Odd |
Either two previous cases work |
Sine-Even and Cosine-Even |
Manipulate sine powers to (sin2(x))p |
Sine Pythagorean Id. |
Expand and apply integral linearity |
Solve cosine cases |
Sine-Cosine Same |
Manipulate powers to (sin(x)cos(x))p |
Sine Double-Angle Id. |
Solve sine cases |
Secant-Odd and Tangent-Even |
Manipulate tangent powers to (tan2(x))p |
Tangent Pythagorean Id. |
Expand and apply integral linearity |
Solve secant cases |
Secant-Even and Tangent-Odd |
Manipulate powers to sec(x)tan(x)secp(x)tanq(x) |
Manipulate tangent powers to (tan2(x))r |
Tangent Pythagorean Id. |
Let u=sec(x) |
Secant-Odd and Tangent-Odd |
Same as previous case |
Secant-Even and Tangent-Even |
Manipulate secant powers to sec2(x)(sec2(x))p |
Secant Pythagorean Id. |
Let u=tan(x) |
Secant-Tangent Same |
Same as previous two cases |
Cosecant-Odd and Cotangent-Even |
Manipulate cotangent powers to (cot2(x))p |
Cotangent Pythagorean Id. |
Expand and apply integral linearity |
Solve cosecant cases |
Cosecant-Even and Cotangent-Odd |
Manipulate powers to csc(x)cot(x)cscp(x)cotq(x) |
Manipulate cotangent powers to (cot2(x))r |
Cotangent Pythagorean Id. |
Let u=csc(x) |
Cosecant-Odd and Cotangent-Odd |
Same as previous case |
Cosecant-Even and Cotangent-Even |
Manipulate cosecant powers to csc2(x)(csc2(x))p |
Cosecant Pythagorean Id. |
Let u=cot(x) |
Cosecant-Cotangent Same |
Same as previous two cases |
p, q, r ∈ ℕ1 = {1,2,3,4,5,...}
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