Pythagorean Identity and Basic Trig Identities

Grade 10·20 problems·~30 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

$Unit circle with point P at angle θ, showing x-projection labeled cos θ and y-projection labeled sin θ.$

A point on the unit circle at angle θ 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 $y = \csc\theta$

$Unit circle with left half (Q2 and Q3) in red labeled cos θ < 0, and right half (Q1 and Q4) in teal labeled cos θ > 0.$

In which quadrants is cosine negative?

Quadrants I and II

Quadrants II and III

Quadrants III and IV

Quadrants I and IV

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.

Which expression is equivalent to $\frac{\sin\theta}{\cos\theta}$ ?

$\sec\theta$

$\csc\theta$

$\tan\theta$

$\cot\theta$

Simplify: $\sin\theta \cdot \sec\theta$ .

$\cos\theta$

$\tan\theta$

$\csc\theta$

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