Back to Exercise: Prove and use Pythagorean identity

Exercises: Pythagorean Identity: Proof and Applications

Grade 9·21 problems·~35 min·Common Core Math - HS Functions·group·hsf-tf-c-8

Work through problems with immediate feedback

Recall / Warm-Up

On the unit circle, a point at angle $\theta$ has coordinates $(x, y)$ .
Which of the following correctly identifies $\sin\theta$ and $\cos\theta$ ?

$\sin\theta = x$ and $\cos\theta = y$

$\sin\theta = y$ and $\cos\theta = x$

$\sin\theta = \frac{y}{x}$ and $\cos\theta = \frac{x}{y}$

$\sin\theta = \frac{x}{y}$ and $\cos\theta = \frac{y}{x}$

In which quadrant are both $\sin\theta$ and $\cos\theta$ negative?

Quadrant I

Quadrant II

Quadrant III

Quadrant IV

The unit circle is the set of all points $(x, y)$ satisfying a specific
equation. A point on the unit circle satisfies $x^{2} + y^{2} = $ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ .
Enter your answer.

Fluency Practice

Given $\cos\theta = \dfrac{4}{5}$ and $\theta$ is in Quadrant I, use
the Pythagorean identity to find $\sin\theta$ . Express your answer as
a fraction in simplest form.

Given $\sin\theta = -\dfrac{5}{13}$ and $\theta$ is in Quadrant III,
use the Pythagorean identity to find $\cos\theta$ . Express your answer
as a fraction in simplest form.

Given $\cos\theta = -\dfrac{2}{3}$ and $\theta$ is in Quadrant II,
use the Pythagorean identity to find $\sin\theta$ . Express your answer
in simplest radical form (e.g., write sqrt(5)/3 for $\dfrac{\sqrt{5}}{3}$ ).

Given $\cos\theta = \dfrac{3}{5}$ and $\theta$ is in Quadrant I, find
$\tan\theta$ . Express your answer as a fraction in simplest form.
(Hint: first find $\sin\theta$ , then use $\tan\theta = \sin\theta / \cos\theta$ .)

Given $\sin\theta = \dfrac{5}{13}$ and $\theta$ is in Quadrant II, find
$\tan\theta$ . Express your answer as a fraction in simplest form.

You're viewing 2 of 6 sections.

Create a free account to continue the full exercise set and save your progress.

Create free account

0 of 8 answered

Answer all problems to submit.

Was this practice set helpful?

Report a problem with this page