18 min read

Special Angles

The exact sin, cos, and tan values for 0°, 30°, 45°, 60°, and 90° come up again and again.

Why These Angles Matter

Five angles appear so often in trigonometry that it helps to know their exact values without a calculator: 0 °, 30 °, 45 °, 60 °, and 90 °.

Notice sin and cos swap values between 30 ° and 60 ° — this is not a coincidence, and you will meet the reason later in this course.

Example 1 — using a special angle directly

Find the exact value of sin(30 °) + cos(60 °). 1 sin(30 °) = 0.5 2 cos(60 °) = 0.5 3 Add: 0.5 + 0.5 = 1 Answer: 1

Practice

Find sin(45 °) \times cos(45 °). Round to 2 decimal places.

Your answer

18 min read

The exact sin, cos, and tan values for 0°, 30°, 45°, 60°, and 90° come up again and again.

Five angles appear so often in trigonometry that it helps to know their exact values without a calculator: 0 °, 30 °, 45 °, 60 °, and 90 °.

Notice sin and cos swap values between 30 ° and 60 ° — this is not a coincidence, and you will meet the reason later in this course.

Example 1 — using a special angle directly

Find the exact value of sin(30 °) + cos(60 °). 1 sin(30 °) = 0.5 2 cos(60 °) = 0.5 3 Add: 0.5 + 0.5 = 1 Answer: 1

Practice

Find sin(45 °) \times cos(45 °). Round to 2 decimal places.

Your answer