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 ☞ ✌ ✡ + ☛ .