How do you remember trigonometric ratios?

Use 'SOH-CAH-TOA': Sin=Opposite/Hypotenuse, Cos=Adjacent/Hypotenuse, Tan=Opposite/Adjacent. For standard values, remember sin: 0, 1/2, 1/√2, √3/2, 1 for 0°, 30°, 45°, 60°, 90°. Cos is sin in reverse order. tan = sin/cos.

What are the three Pythagorean identities in trigonometry?

Three fundamental identities: (1) sin²θ + cos²θ = 1 (most important — used in most proofs). (2) 1 + tan²θ = sec²θ (derived by dividing first by cos²θ). (3) 1 + cot²θ = cosec²θ (derived by dividing first by sin²θ). From (1): sin²θ = 1−cos²θ; sec²θ−tan²θ = 1; cosec²θ−cot²θ = 1.

What is the value of sin 45°, cos 30°, and tan 60°?

sin 45° = 1/√2 = √2/2 ≈ 0.707. cos 30° = √3/2 ≈ 0.866. tan 60° = √3 ≈ 1.732. These are the most commonly asked standard values. Note: sin 30° = cos 60° = 1/2, and sin 60° = cos 30° = √3/2 (complementary angles).

Trigonometric Ratios

Introduction to Trigonometry • Class 10 Mathematics • NCERT • CBSE

Trigonometric ratios relate the angles of a right-angled triangle to the ratios of its sides. For angle θ: sinθ = opposite/hypotenuse, cosθ = adjacent/hypotenuse, tanθ = opposite/adjacent. Key values: sin30°=½, sin45°=1/√2, sin60°=√3/2.

Key Formulas

sin θ = Opposite/Hypotenuse (SOH)
cos θ = Adjacent/Hypotenuse (CAH)
tan θ = Opposite/Adjacent (TOA)
sin²θ + cos²θ = 1
1 + tan²θ = sec²θ
1 + cot²θ = cosec²θ
sin(90°−θ) = cosθ; cos(90°−θ) = sinθ

Frequently Asked Questions

How do you remember trigonometric ratios?: Use 'SOH-CAH-TOA': Sin=Opposite/Hypotenuse, Cos=Adjacent/Hypotenuse, Tan=Opposite/Adjacent. For standard values, remember sin: 0, 1/2, 1/√2, √3/2, 1 for 0°, 30°, 45°, 60°, 90°. Cos is sin in reverse order. tan = sin/cos.
What are the three Pythagorean identities in trigonometry?: Three fundamental identities: (1) sin²θ + cos²θ = 1 (most important — used in most proofs). (2) 1 + tan²θ = sec²θ (derived by dividing first by cos²θ). (3) 1 + cot²θ = cosec²θ (derived by dividing first by sin²θ). From (1): sin²θ = 1−cos²θ; sec²θ−tan²θ = 1; cosec²θ−cot²θ = 1.
What is the value of sin 45°, cos 30°, and tan 60°?: sin 45° = 1/√2 = √2/2 ≈ 0.707. cos 30° = √3/2 ≈ 0.866. tan 60° = √3 ≈ 1.732. These are the most commonly asked standard values. Note: sin 30° = cos 60° = 1/2, and sin 60° = cos 30° = √3/2 (complementary angles).

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