Equations Containing Trigonometric Functions and Arbitrary Parameters
1.7. Equations Containing Trigonometric Functions and Arbitrary Parameters
1.7.1. Equations Containing a Cosine
2 ✆ +( cos + ) .
This is a special case of equation 1.8.1.1 with ✠ ( ✡ )= ✍ cos ☞ ✌ ✡ + ☛ .
+( 2 ✟ cos
This is a special case of equation 1.8.1.6 with ✠ ( ✡ )= ☛ and ✎ ( ✡ )= ✍ cos ☞ ✌ ✡ .
cos
This is a special case of equation 1.8.1.3 with ✠ ( ✡ )= ✍ cos ☞ ✌ ✡ + ☛ .
+( ✆ cos
This is a special case of equation 1.8.1.7 with ✠ ( ✡ )= ☛ cos ☞ ✌ ✡ .
This is a special case of equation 1.8.2.1 with ✠ ( ✡ )= ✍ cos ☞ ✌ ✡ + ☛ .
+ ( ✟ cos
This is a special case of equation 1.8.2.3 with ✠ ( ✡ )= ✍ cos ☞ ✌ ✡ + ☛ .
This is a special case of equation 1.8.3.1 with ✠ ( ✡ )= ✍ and ✎ ( ✡ )= ☛ cos ☞ ✌ ✡ + ✏ .
cos
This is a special case of equation 1.8.2.6 with ✠ ( ✡ )= ☛ cos ☞ ✌ ✡ .
+( 2 ✟ cos
This is a special case of equation 1.8.4.1 with ✠ ( ✡ )= ✍ cos ☞ ✌ ✡ and ✎ ( ✡ )= ☛ .
= ✄ 2 ☎ 2 +( ✟ cos
This is a special case of equation 1.8.4.2 with ✠ ( ✡ )= ✍ cos ☞ ✌ ✡ + ☛ .
= ✄ 4 ☎ 2 +( ✟ cos
This is a special case of equation 1.8.8.4 with ✠ ( ✡ )= ✓ and ✎ ( ✡ )= ✍ cos ☞ ✌ ✡ + ☛ .
+ ( ✟ cos
This is a special case of equation 1.8.4.5 with ✠ ( ✡ )= ✍ cos ☞ ✌ ✡ + ☛ .
1.7.2. Equations Containing a Sine
+( 2 ✟ sin
This is a special case of equation 1.8.1.1 with ✠ ( ✡ )= ✍ sin ☞ ✌ ✡ + ☛ .
This is a special case of equation 1.8.1.6 with ✠ ( ✡ )= ☛ and ✎ ( ✡ )= ✍ sin ☞ ✌ ✡ .
( 2 ✟ + sin
This is a special case of equation 1.8.1.3 with ✠ ( ✡ )= ✍ sin ☞ ✌ ✡ + ☛ .
+( 2 ✆ sin
This is a special case of equation 1.8.1.7 with ✠ ( ✡ )= ☛ sin ☞ ✌ ✡ .
This is a special case of equation 1.8.2.1 with ✠ ( ✡ )= ✍ sin ☞ ✌ ✡ + ☛ .
+ ( ✟ sin
This is a special case of equation 1.8.2.3 with ✠ ( ✡ )= ✍ sin ☞ ✌ ✡ + ☛ .
This is a special case of equation 1.8.3.1 with ✠ ( ✡ )= ✍ and ✎ ( ✡ )= ☛ sin ☞ ✌ ✡ + ✏ .
sin
This is a special case of equation 1.8.2.6 with ✠ ( ✡ )= ☛ sin ☞ ✌ ✡ .
+( 2 ✟ sin
This is a special case of equation 1.8.4.1 with ✠ ( ✡ )= ✍ sin ☞ ✌ ✡ and ✎ ( ✡ )= ☛ .
= ✄ 2 ☎ 2 +( ✟ sin
This is a special case of equation 1.8.4.2 with ✠ ( ✡ )= ✍ sin ☞ ✌ ✡ + ☛ .
= ✄ 4 ☎ 2 +( ✟ sin
This is a special case of equation 1.8.8.4 with ✠ ( ✡ )= ✓ and ✎ ( ✡ )= ✍ sin ☞ ✌ ✡ + ☛ .
+ ( ✟ sin
This is a special case of equation 1.8.4.5 with ✠ ( ✡ )= ✍ sin ☞ ✌ ✡ + ☛ .
1.7.3. Equations Containing a Tangent
+( 2 ✟ tan
This is a special case of equation 1.8.1.1 with ✠ ( ✡ )= ✍ tan ☞ ✌ ✡ + ☛ .
This is a special case of equation 1.8.1.6 with ✠ ( ✡ )= ☛ and ✎ ( ✡ )= ✍ tan ☞ ✌ ✡ .
( 2 ✟ + tan
This is a special case of equation 1.8.1.3 with ✠ ( ✡ )= ✍ tan ☞ ✌ ✡ + ☛ .
+( 2 ✆ tan
This is a special case of equation 1.8.1.7 with ✠ ( ✡ )= ☛ tan ☞ ✌ ✡ .
This is a special case of equation 1.8.2.1 with ✠ ( ✡ )= ✍ tan ☞ ✌ ✡ + ☛ .
+ ( ✟ tan
This is a special case of equation 1.8.2.3 with ✠ ( ✡ )= ✍ tan ☞ ✌ ✡ + ☛ .
This is a special case of equation 1.8.3.1 with ✠ ( ✡ )= ✍ and ✎ ( ✡ )= ☛ tan ☞ ✌ ✡ + ✏ .
tan
This is a special case of equation 1.8.2.6 with ✠ ( ✡ )= ☛ tan ☞ ✌ ✡ .
+( 2 ✟ tan
This is a special case of equation 1.8.4.1 with ✠ ( ✡ )= ✍ tan ☞ ✌ ✡ and ✎ ( ✡ )= ☛ .
= ✄ 2 ☎ 2 +( ✟ tan
This is a special case of equation 1.8.4.2 with ✠ ( ✡ )= ✍ tan ☞ ✌ ✡ + ☛ .
= ✄ 4 ☎ 2 +( ✟ tan
This is a special case of equation 1.8.8.4 with ✠ ( ✡ )= ✓ and ✎ ( ✡ )= ✍ tan ☞ ✌ ✡ + ☛ .
+ ( ✟ tan
This is a special case of equation 1.8.4.5 with ✠ ( ✡ )= ✍ tan ☞ ✌ ✡ + ☛ .
1.7.4. Equations Containing a Cotangent
+( 2 ✟ cot
This is a special case of equation 1.8.1.1 with ✠ ( ✡ )= ✍ cot ☞ ✌ ✡ + ☛ .
This is a special case of equation 1.8.1.6 with ✠ ( ✡ )= ☛ and ✎ ( ✡ )= ✍ cot ☞ ✌ ✡ .
( 2 ✟ + cot
This is a special case of equation 1.8.1.3 with ✠ ( ✡ )= ✍ cot ☞ ✌ ✡ + ☛ .
+( 2 ✆ cot
This is a special case of equation 1.8.1.7 with ✠ ( ✡ )= ☛ cot ☞ ✌ ✡ .
+( ✟ cot
This is a special case of equation 1.8.2.1 with ✠ ( ✡ )= ✍ cot ☞ ✌ ✡ + ☛ .
cot
This is a special case of equation 1.8.2.3 with ✠ ( ✡ )= ✍ cot ☞ ✌ ✡ + ☛ .
This is a special case of equation 1.8.3.1 with ✠ ( ✡ )= ✍ and ✎ ( ✡ )= ☛ cot ☞ ✌ ✡ + ✏ .
cot
This is a special case of equation 1.8.2.6 with ✠ ( ✡ )= ☛ cot ☞ ✌ ✡ .
This is a special case of equation 1.8.4.1 with ✠ ( ✡ )= ✍ cot ☞ ✌ ✡ and ✎ ( ✡ )= ☛ .
+( 2 ✟ cot
This is a special case of equation 1.8.4.2 with ✠ ( ✡ )= ✍ cot ☞ ✌ ✡ + ☛ .
= ✄ 4 ☎ 2 +( ✟ cot
This is a special case of equation 1.8.8.4 with ✠ ( ✡ )= ✓ and ✎ ( ✡ )= ✍ cot ☞ ✌ ✡ + ☛ .
+ ( ✟ cot
This is a special case of equation 1.8.4.5 with ✠ ( ✡ )= ✍ cot ☞ ✌ ✡ + ☛ .