$\sin^2\theta + \cos^2\theta$ equals:
A$2$
B$0$
C$\tan\theta$
D$1$
Answer & Solution
Correct answer: D. $1$
The **Pythagorean identity** $\sin^2\theta + \cos^2\theta = 1$ holds for every real $\theta$.
It comes from Pythagoras applied to the unit circle: any point on it has coordinates $(\cos\theta, \sin\theta)$ with distance 1 from origin
so the sum of squared coordinates is 1.
Companion identities:
- Dividing by $\cos^2\theta$: $1 + \tan^2\theta = \sec^2\theta$.
- Dividing by $\sin^2\theta$: $\cot^2\theta + 1 = \csc^2\theta$.
Keep practising Unit 3A: Chain Rule and Composite Functions
Browse all Unit 3A: Chain Rule and Composite Functions questions for AP Calculus AB, or explore more Mathematics topics.
Related questions
In which quadrant is sin θ positive and cos θ negative?If tan θ + cot θ = 2, find sin 2θ:General solution of sin θ = sin α:In triangle with sides 7, 8, 9, find cos of the angle opposite to side 9 (use cosine rule)If sin θ = 12/13 (acute), find tan(θ/2):General solution of cos θ = 0:If sin θ + cos θ = 1, then sin θ × cos θ equals:In triangle ABC with sides a, b, c opposite to angles A, B, C: sine rule states: