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Back to Exercise: Pythagorean identity and basic trig identities

Pythagorean Identity and Basic Trig Identities

Grade 10·20 problems·~30 min·ACT Math·topic·act-geo-trig-pythagid
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A

Recall / Warm-Up

1.

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

Unit circle with point P at angle θ, showing x-projection labeled cos θ and y-projection labeled sin θ.
2.

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

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.
3.

In which quadrants is cosine negative?

B

Fluency Practice

1.

If sin⁡θ=35\sin\theta = \frac{3}{5} and θ\theta is in Quadrant I, what is cos⁡θ\cos\theta? Express your answer as a fraction.

2.

If cos⁡θ=513\cos\theta = \frac{5}{13} and θ\theta is in Quadrant I, what is sin⁡θ\sin\theta? Express your answer as a fraction.

3.

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

4.

Which expression is equivalent to sin⁡θcos⁡θ\frac{\sin\theta}{\cos\theta}?

5.

Simplify: sin⁡θ⋅sec⁡θ\sin\theta \cdot \sec\theta.

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