Topic Details (Notes format)

How to Use the Pythagorean Identities in Trigonometry

Subject: Mathematics

Book: Maths Mastery

Key Pythagorean trig identities include sin²(θ) + cos²(θ) = 1, 1 + tan²(θ) = sec²(θ), and 1 + cot²(θ) = csc²(θ). These relationships allow you to convert between trigonometric functions or simplify complicated expressions. For example, if sin(θ) = 3/5, then cos(θ) = √(1 – sin²(θ)) = √(1 – 9/25) = √(16/25) = 4/5. This knowledge extends to verifying trigonometric proofs, analyzing wave functions in physics, or building engineering models that rely on sinusoidal behaviors. Familiarity with Pythagorean identities significantly eases advanced problem-solving in calculus and beyond.

Practice Questions

A triangle has angles 60°, 60°, and 60°. What type of triangle is it?

View Question

If a+b = 10 and ab = 21, what is the value of a^3 + b^3?

View Question

A car covers a distance of 150 km in 2.5 hours. What is its average speed?

View Question

If x:y = 4:5 and y:z = 2:3, what is x:z?

View Question

The perimeter of a rectangle is 50 cm, and its length is 15 cm. What is its width?

View Question

A number is increased by 20% and then decreased by 10%. What is the net change?

View Question

What is the sum of all even numbers between 1 and 50?

View Question

What is the square root of 144?

View Question

What is the sum of the interior angles of a hexagon?

View Question

The probability of getting an even number when rolling a die is:

View Question