The Pythagorean Identity

Pythagoras, on a circle of radius 1.

10 problems · about 20 minutes · F-TF.C.8

NameDate

Figure — use these to answer the problems

The two legs are the coordinates, and the hypotenuse is always 1.

Angle in degrees45

Figure 1

From earlier lessons. Loosen up before the new work.

2 problems

From “Composing Functions and Inverses”
What is arcsin(sin 170°), in degrees?
Answer
From “Solving Trigonometric Equations”
sin θ = 0.866 gives 60°. The other solution below 360°, in degrees?
Answer

Straightforward practice. Get the method working first.

4 problems

sin θ = 0.28 and cos²θ = 1 − 0.0784. What is cos²θ?
Answer
4
Where does sin²θ + cos²θ = 1 come from?
- Pythagoras, on a triangle with hypotenuse 1.
- It is a separate new fact.
cos θ = 0.6, θ acute. What is sin θ?
Answer
sin θ = 0, θ = 0. What is cos θ?
Answer

The same ideas with more to keep track of.

2 problems

Mixed problems. Work out what kind of question it is before you start.

2 problems