Back to Exercise: Pythagorean identity and basic trig identities

Pythagorean Identity and Basic Trig Identities

Grade 10·25 problems·~37 min·ACT Math·topic·act-geo-trig-pythagid

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Recall / Warm-Up

In a right triangle, which ratio defines $\sin\theta$ ?

opposite / hypotenuse

adjacent / hypotenuse

opposite / adjacent

hypotenuse / opposite

$Unit circle with point P at angle θ in Quadrant I, labeled (x, y), with dashed projections to the x-axis and y-axis.$

A point on the unit circle at angle $\theta$ has coordinates $(x, y)$ . Which statement is correct?

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

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

$x = \tan\theta$ and $y = \sec\theta$

$x = \sec\theta$ and $y = \csc\theta$

$Unit circle with x and y axes and the four quadrants labeled with Roman numerals I through IV.$

In which quadrants is cosine negative?

Quadrants I and II

Quadrants II and III

Quadrants III and IV

Quadrants I and IV

Fluency Practice

If $\sin\theta = \frac{3}{5}$ and $\theta$ is in Quadrant I, what is $\cos\theta$ ? Express your answer as a fraction.

If $\cos\theta = \frac{5}{13}$ and $\theta$ is in Quadrant I, what is $\sin\theta$ ? Express your answer as a fraction.

If $\tan\theta = 2$ and $\theta$ is in Quadrant I, what is $\sec\theta$ ? Express your answer in simplified radical form.

If $\sin\theta = \frac{5}{13}$ and $\theta$ is in Quadrant II, what is $\tan\theta$ ?

$\frac{5}{12}$

$-\frac{12}{5}$

$-\frac{13}{12}$

$-\frac{5}{12}$

If $\tan\theta = 2$ and $\theta$ is in Quadrant I, what is $\sin\theta$ ? Express your answer in simplified radical form with a rationalized denominator.

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